Systems and methods for determining an appropriate model parameter order

ABSTRACT

Systems and methods for determining an appropriate parameter order for a building energy use model are provided. A described method includes receiving an energy use model for a building site, obtaining a plurality of data points, calculating a first regression statistic indicating a fit of the energy use model to the plurality of data points under a null hypothesis and a second regression statistic indicating a fit of the energy use model to the plurality of data points under an alternative hypothesis, and comparing a test statistic to a threshold value. The test statistic is a function of the first regression statistic and the second regression statistic. The method further includes determining an appropriate parameter order for the energy use model based on a result of the comparison.

BACKGROUND

The present disclosure relates generally to systems and methods foranalyzing energy consumption model data. The present disclosure relatesmore particularly to systems and methods for determining an appropriatenumber of parameters (e.g., regression coefficients and/or balance pointparameters) for a building energy use model.

Many buildings are equipped with a variety of energy-consuming equipmentand devices. For example, a building may be equipped with heating,ventilation, and air conditioning (HVAC) equipment that consume energyto regulate the temperature, humidity, and/or air quality in thebuilding. Other exemplary types of energy-consuming building equipmentinclude lighting fixtures, security equipment, data networkinginfrastructure, and other such equipment.

The energy efficiency of buildings has become an area of interest inrecent years. For an energy provider, a high energy efficiency of thebuildings that it services helps to alleviate strains placed on theenergy provider's electrical generation and transmission assets. For abuilding operator, a high energy efficiency corresponds to greaterfinancial savings because less energy is consumed by the building.

One way to improve the energy efficiency of a building is through anaccurate model of the building's energy use. An energy use model for abuilding typically predicts the building's total energy consumption as afunction of one or more predictor variables and one or more modelparameters. The number and type of parameters included in the energy usemodel may depend on the physical location of the building and othercharacteristics of the building site. It is often difficult andchallenging to accurately determine an appropriate parameter order for abuilding energy use model.

SUMMARY

One implementation of the present disclosure is a method for determiningan appropriate parameter order for an energy use model for a buildingsite. The method includes receiving an energy use model for a buildingsite. The energy use model may include a weather-related predictorvariable. The method further includes obtaining a plurality of datapoints. Each of the data points may include a value of theweather-related predictor variable and an associated energy consumptionvalue for the building site. The method further includes calculating afirst regression statistic indicating a fit of the energy use model tothe plurality of data points under a null hypothesis, calculating asecond regression statistic indicating a fit of the energy use model tothe plurality of data points under an alternative hypothesis, andcomparing a test statistic to a threshold value. The test statistic is afunction of the first regression statistic and the second regressionstatistic. The method further includes determining an appropriateparameter order for the energy use model based on a result of thecomparison.

In some embodiments, obtaining the plurality of data points includes,for each of the data points, receiving at least one of an observedtemperature value and an observed enthalpy value and calculating thevalue of the weather-related predictor variable using the observedtemperature value or the observed enthalpy value. In some embodiments,the weather-related predictor variable is at least one of cooling degreedays, heating degree days, cooling energy days, heating energy days,temperature, and enthalpy.

In some embodiments, the energy use model includes a balance pointparameter under the alternative hypothesis and does not include abalance point parameter under the null hypothesis. In some embodiments,the balance point parameter is at least one of a temperature parameterhaving a temperature value between a minimum and a maximum of aplurality of observed temperature values and an enthalpy parameterhaving an enthalpy value between a minimum and a maximum of a pluralityof observed enthalpy values. In some embodiments, the value of theweather-related predictor variable is a function of the balance pointparameter. In some embodiments, the energy use model under the nullhypothesis is nested within the energy use model under the alternativehypothesis. For example, under the alternative hypothesis, the energyuse model may use an extra parameter (i.e., a balance point parameter)relative to the energy use model under the null hypothesis. The balancepoint parameter may contribute to the energy consumption predicted bythe energy use model by affecting the value of the weather-relatedpredictor variable without appearing explicitly in the energy use model.

In some embodiments, the first regression statistic is a sum of squarederror under the null hypothesis and the second regression statistic is asum of squared error under the alternative hypothesis. The sum ofsquared error may be a function of a difference between an energyconsumption of the building site predicted by the energy use model andan actual energy consumption of the building site.

In some embodiments, the test statistic is a ratio of (a) an improvementbetween the first regression statistic and the second regressionstatistic to (b) the second regression statistic divided by a number ofdegrees of freedom of the second regression statistic.

In some embodiments, the method further includes identifying asignificance level and calculating the threshold value. The thresholdvalue may be a function of the identified significance level. In someembodiments, the function of the identified significance level is aninverse F-distribution function based on the identified significancelevel, a number of degrees of freedom of the second regressionstatistic, and a difference between a number of degrees of freedom ofthe first regression statistic and the number of degrees of freedom ofthe second regression statistic.

In some embodiments, determining the appropriate parameter order for theenergy use model includes rejecting the null hypothesis if the result ofthe comparison reveals that test statistic is not less than thethreshold value and failing to reject the null hypothesis if the resultof the comparison reveals that the test statistic is less than thethreshold value. In some embodiments, determining the appropriateparameter order for the energy use model includes determining that athree-parameter model is appropriate in response to rejecting the nullhypothesis and determining that a two-parameter model is appropriate inresponse to failing to reject the null hypothesis. In some embodiments,determining an appropriate parameter order for the energy use modelincludes identifying the building site as at least one of a buildingsite for which heating is not required and a building site for whichcooling is not required in response to failing to reject the nullhypothesis.

In some embodiments, the method further includes identifying a currentparameter order of the energy use model, comparing the current parameterorder with the appropriate parameter order, updating the energy usemodel with an energy use model having the appropriate parameter order inresponse to the current parameter order not matching the appropriateparameter order, and storing the energy use model for the building site.The stored energy use model may have the appropriate parameter order.

In some embodiments, the method further includes using the stored energyuse model to perform a peer analysis of energy use model parameters fora class of buildings, calculating a difference between an energy usemodel parameter of the stored energy use model and a mean of the energyuse model parameters of the class of buildings, and detecting an outliermodel parameter based on a result of the calculation.

In some embodiments, the method further includes monitoring changes toone or more energy use model parameters in the stored energy use model,detecting the existence of a fault condition using a monitored change tothe energy use model parameters, and determining a change to an energyconsumption that results from the fault condition based on the change tothe energy use model parameters.

In some embodiments, the method further includes updating the energy usemodel with an energy use model having the appropriate parameter order,applying inputs to the updated energy use model, conducting aperformance analysis using the updated energy use model, and providingan output using a result of the performance analysis.

Another implementation of the present disclosure is a system fordetermining an appropriate parameter order for an energy use model for abuilding site. The system includes a communications interface configuredto receive an energy use model for a building site. The energy use modelmay include a weather-related predictor variable. The system furtherincludes a processing circuit configured to obtain a plurality of datapoints, calculate a first regression statistic indicating a fit of theenergy use model to the plurality of data points under a nullhypothesis, and calculate a second regression statistic indicating a fitof the energy use model to the plurality of data points under analternative hypothesis. Each of the data points may include a value ofthe weather-related predictor variable and an associated energyconsumption value for the building site. The processing circuit isfurther configured to compare a test statistic to a threshold value andto determine an appropriate parameter order for the energy use modelbased on a result of the comparison. The test statistic is a function ofthe first regression statistic and the second regression statistic.

In some embodiments, obtaining the plurality of data points includes,for each of the data points, receiving at least one of an observedtemperature value and an observed enthalpy value and calculating thevalue of the weather-related predictor variable using the observedtemperature value or the observed enthalpy value. In some embodiments,the weather-related predictor variable is at least one of cooling degreedays, heating degree days, cooling energy days, heating energy days,temperature, and enthalpy.

In some embodiments, the energy use model includes a balance pointparameter under the alternative hypothesis and does not include abalance point parameter under the null hypothesis. In some embodiments,the balance point parameter is at least one of a temperature parameterhaving a temperature value between a minimum and a maximum of aplurality of observed temperature values and an enthalpy parameterhaving an enthalpy value between a minimum and a maximum of a pluralityof observed enthalpy values. In some embodiments, the value of theweather-related predictor variable is a function of the balance pointparameter. In some embodiments, the energy use model under the nullhypothesis is nested within the energy use model under the alternativehypothesis.

In some embodiments, the first regression statistic is a sum of squarederror under the null hypothesis and the second regression statistic is asum of squared error under the alternative hypothesis. The sum ofsquared error may be a function of a difference between an energyconsumption of the building site predicted by the energy use model andan actual energy consumption of the building site.

In some embodiments, the test statistic is a ratio of (a) an improvementbetween the first regression statistic and the second regressionstatistic to (b) the second regression statistic divided by a number ofdegrees of freedom of the second regression statistic.

In some embodiments, the processing circuit is further configured toidentify a significance level and calculate the threshold value. Thethreshold value may be a function of the identified significance level.In some embodiments, the function of the identified significance levelis an inverse F-distribution function based on the identifiedsignificance level, a number of degrees of freedom of the secondregression statistic, and a difference between a number of degrees offreedom of the first regression statistic and the number of degrees offreedom of the second regression statistic.

In some embodiments, determining the appropriate parameter order for theenergy use model includes rejecting the null hypothesis if the result ofthe comparison reveals that test statistic is not less than thethreshold value and failing to reject the null hypothesis if the resultof the comparison reveals that the test statistic is less than thethreshold value. In some embodiments, determining the appropriateparameter order for the energy use model includes determining that athree-parameter model is appropriate in response to rejecting the nullhypothesis and determining that a two-parameter model is appropriate inresponse to failing to reject the null hypothesis. In some embodiments,determining an appropriate parameter order for the energy use modelincludes identifying the building site as at least one of a buildingsite for which heating is not required and a building site for whichcooling is not required in response to failing to reject the nullhypothesis.

In some embodiments, the processing circuit is further configured toidentify a current parameter order of the energy use model, compare thecurrent parameter order with the appropriate parameter order, update theenergy use model with an energy use model having the appropriateparameter order in response to the current parameter order not matchingthe appropriate parameter order, and store the energy use model for thebuilding site. The stored energy use model may have the appropriateparameter order.

In some embodiments, the processing circuit is further configured to usethe stored energy use model to perform a peer analysis of energy usemodel parameters for a class of buildings, calculate a differencebetween an energy use model parameter of the stored energy use model anda mean of the energy use model parameters of the class of buildings, anddetect an outlier model parameter based on a result of the calculation.

In some embodiments, the processing circuit is further configured tomonitor changes to one or more energy use model parameters in the storedenergy use model, detect the existence of a fault condition using amonitored change to the energy use model parameters, and determine achange to an energy consumption that results from the fault conditionbased on the change to the energy use model parameters.

In some embodiments, the processing circuit is further configured toupdate the energy use model with an energy use model having anappropriate parameter order, apply inputs to the updated energy usemodel, conduct a performance analysis using the updated energy usemodel, and provide an output using a result of the performance analysis.

Those skilled in the art will appreciate that the summary isillustrative only and is not intended to be in any way limiting. Otheraspects, inventive features, and advantages of the devices and/orprocesses described herein, as defined solely by the claims, will becomeapparent in the detailed description set forth herein and taken inconjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a drawing of a building data acquisition system includingbuildings, a network, a historical weather data source, a utility, and abuilding analysis system, according to an exemplary embodiment

FIG. 2 is an illustration of an energy use profile for a building orbuilding site, according to an exemplary embodiment.

FIG. 3 is a block diagram illustrating the building analysis system ofFIG. 1 in greater detail, according to an exemplary embodiment.

FIG. 4 is a flowchart of a process for determining an appropriateparameter order for a building energy use model is shown, according toan exemplary embodiment.

DETAILED DESCRIPTION

Before turning to the FIGURES, it should be understood that thedisclosure is not limited to the details or methodology set forth in thedescription or illustrated in the FIGURES. It should also be understoodthat the terminology is for the purpose of description only and shouldnot be regarded as limiting.

Referring generally to the FIGURES, systems and methods for determiningan appropriate parameter order for a building energy use model areshown, according to various exemplary embodiments. Building energy usemodels may take a variety of forms including parametric models (e.g.,linear regression, non-linear regression, etc.), non-parametric models(e.g., neural networks, kernel estimation, Bayesian, etc.) or somethingin between (e.g., Gaussian process models, etc.). A building energy usemodel may describe the energy usage of a building or building site interms of one or more independent variables (e.g., weather data,occupancy data, etc.) and one or more model parameters.

Building energy use models may be classified based on the parameterorder of the model (e.g., number of parameters, number of parametervectors, etc.). For example, the energy usage of some buildings orbuilding sites may be described using a one-parameter model in whichenergy use is restricted to a baseline energy consumption (e.g.,ignoring independent variables such as outside air temperature, buildingoccupancy, etc.). Other buildings or building sites may warrant atwo-parameter model (e.g., a baseline energy consumption and either aheating profile or a cooling profile), a three-parameter model (e.g., abaseline energy consumption and either a heating profile or a coolingprofile having a break even temperature or balance point), afour-parameter model (e.g., a baseline energy consumption and both aheating profile and a cooling profile, where both the heating profileand the cooling profile have a shared balance point), a five-parametermodel (e.g., a baseline energy consumption and both a heating profileand a cooling profile, where the heating profile and the cooling profilehave different balance points), or an energy use model having a higherparameter order.

The appropriate parameter order for a building energy use model maydepend on the physical characteristics of the building or building site.For example, a two-parameter model may be distinguished from athree-parameter model by determining whether the energy use model has abreak even temperature or balance point. The break even temperature orbalance point may be a threshold outside air temperature at whichheating or cooling is no longer required to maintain the temperature ofthe air in the building within an acceptable temperature range.

For buildings located in temperate climates (e.g., climates in which theoutside air temperature is often within or near the acceptabletemperature range), the break even temperature may be determined byinspecting energy use data associated with the building. For example, byexamining building energy usage as a function of outside airtemperature, the break even temperature can be identified as thetemperature at which energy usage no longer depends on the outside airtemperature. A three-parameter model may have the appropriate parameterorder to accurately model buildings or building sites having a breakeven temperature.

For buildings located in extreme climates (e.g., climates in which theoutside air temperature is consistently hot or consistently cold), itmay be difficult to accurately determine the break even temperaturebecause heating or cooling may be required at all times or nearly alltimes to maintain the temperature of the air in the building within theacceptable temperature range. A two-parameter model may have theappropriate parameter order to accurately model buildings or buildingsites for which a break even temperature is not applicable or cannot bereadily determined from building performance data (e.g., energy usedata, weather data, occupancy data, etc.).

The systems and methods described herein may be used to determine anappropriate parameter order for a building energy use model. In someembodiments, the described systems and methods may be used to determinewhether the energy usage of a building or building site is best modeledusing a two-parameter model or a three-parameter model. Performance datafor the building or building site may be used to construct both atwo-parameter regression model (e.g., without a balance point parameter)and a three-parameter regression model (e.g., with a balance pointparameter) describing the energy use of the building. In someembodiments, the balance point parameter may be set to a fixed value inthe two-parameter regression model such that the total number of unknownparameters in the two-parameter regression model is less than the totalnumber of unknown parameters in the three-parameter regression model.Reducing the number of unknown parameters in a model can help improvethe accuracy of the model. Determining and using an appropriate numberof parameters in the model can also help improve the accuracy of themodel.

Hypothesis testing may be used to determine whether the addition of thevariable balance point parameter in the three-parameter model results ina statistically significant improvement to the fit of the energy usemodel to the performance data. If the fit of three-parameter model issignificantly better than the fit of the two-parameter model, it may bedetermined that a three-parameter model has the appropriate parameterorder for the building or building site. A test statistic based on therespective errors of regression of the two-parameter model and thethree-parameter model may be used to quantify whether the fit of thethree-parameter model is significantly better.

Referring now to FIG. 1, an illustration of a building data acquisitionsystem 100 is shown, according to an exemplary embodiment. Building dataacquisition system 100 may be configured to collect, store, and/oranalyze performance data related to a building's energy use. Theperformance data for the building may be used to model the building'senergy usage, predict related parameters in the energy use model, and/ordetermine an appropriate parameter order for the energy use model.

Building data acquisition system 100 is shown to include buildings102-106. Buildings 102-106 may include any number of buildings (e.g., afirst through a nth building) and any type of buildings (e.g.,commercial buildings, residential buildings, industrial buildings,etc.). For example, building 102 may be an office building, building 104may be a manufacturing facility, and building 106 may be a hospitalityfacility, such as a hotel. Other exemplary buildings in buildings102-106 may include, but are not limited to, data centers, schools,shipping facilities, and government buildings. Buildings 102-106 mayinclude any combination of building types.

Buildings 102-106 may be located within the same geographic regions asone another or across different geographic regions. For example,building 102 and building 104 may be located in the same city, whilebuilding 106 may be located in a different city. Different levels ofgranularity may be used to distinguish buildings 102-106 as beinglocated in the same geographic region. For example, geographic regionsmay be divided by country, state, city, metropolitan area, time zone,zip code, area code, latitude, longitude, growing zone, combinationsthereof, or using any other geographic classification system. In someembodiments, a building's geographic location may be used as a proxy forits climatic zone. For example, data regarding a building's location inHawaii may be used to determine that the building is located in atropical climate.

In some embodiments, each of buildings 102-106 may be part of a buildingsite (e.g., the same building site, separate building sites, etc.). Abuilding site may include one or more of buildings 102-106 and typicallyincludes buildings that are located proximate to each other and/orinterconnected. A single HVAC system, water system, and/or electric gridmay service multiple buildings that are part of the same building site.An energy use model may be developed for individual buildings, for abuilding site, or for both individual buildings and a building site.

Buildings 102-106 may be equipped with sensors and other monitoringdevices configured to measure performance data related to the building'senergy consumption. For example, buildings 102-106 may have devices(e.g., computing devices, power meters, etc.) configured to measure thewater consumption, energy consumption, and energy demand of buildings102-106. Other forms of performance data may include a measuredtemperature in one or more zones of a building, dimensions of thebuilding (e.g., square footage, etc.), and/or any other value thatrelates to the building's energy usage profile. In some embodiments,performance data includes data used in a building automation system. Forexample, performance data may include control parameters (e.g., setpoints, tuning parameters, threshold values, etc.) used to regulate thetemperature in the building and/or timing data used to automaticallyturn on or off lighting within the building (e.g., at night, when thebuilding is unoccupied, according to a set schedule, etc.).

In some embodiments, readily available data may be used to determine andmodel a building's energy consumption. For example, billing datareceived from a utility 114 may be used to determine a building's energyconsumption and the financial costs associated with the energyconsumption. Such an approach may simplify and reduce the cost ofperforming the energy analysis over approaches that rely heavily onsensor data from a building.

In some embodiments, performance data includes weather data for a regionin which buildings 102-106 are located. The weather data may begenerated by weather-sensing equipment at buildings 102-106. Forexample, buildings 102-106 may be equipped with temperature sensors thatmeasure the outside air temperature. In other embodiments, buildings102-106 may be configured to receive weather data from an externalweather data source.

In some embodiments, performance data includes weather data for atypical meteorological year (TMY) received from historical weather datasource 112 (e.g., a computer system of the National Oceanic andAtmospheric Administration or similar data source). In the United Statesof America, the first set of TMY data was collected between 1948-1980from various locations throughout the country. A second set of TMY data(TMY2), which also includes data regarding precipitable moisture, wascollected between 1961-1990. In addition, a third set of TMY data(TMY3), was collected from many more locations than TMY2 data over thespan of 1976-1995. Regardless of the version used, TMY data may be usedto compare current conditions to normal or predicted conditions, in someembodiments. In further embodiments, TMY data may be used to predictfuture conditions of a building (e.g., by using the historical data topredict typical future weather conditions) or future energy consumptionsby a building. For example, TMY data may be used to predict an averageoutdoor temperature change for a building during the upcoming month ofMarch. TMY data may be stored by the building automation systems ofbuildings 102-106 or building analysis system 110 and used to model theheating and cooling needs of buildings 102-106. As used herein, “TMYdata” may refer to any version or set of TMY data (e.g., TMY2 data, TMY3data, etc.).

Performance data may be collected for individual buildings 102-106 orfor a building site. For example, energy usage data (e.g., received fromutility 114 or otherwise) for multiple buildings may be combined into atotal energy usage for a building site. Buildings that are part of thesame building site may share the same outside air temperature, outsideair enthalpy, or other weather-related predictor variables (e.g.,cooling degree days, heating degree days, cooling energy days, heatingenergy days, etc.).

Still referring to FIG. 1, building data acquisition system 100 is shownto include a network 108. Network 108 may be any form of computernetwork that relays information between buildings 102-106 and a buildinganalysis system 110. For example, network 108 may include the Internetand/or other types of data networks, such as a local area network (LAN),a wide area network (WAN), a cellular network, satellite network, orother types of data networks. Network 108 may also include any number ofcomputing devices (e.g., computer, servers, routers, network switches,etc.) that are configured to receive and/or transmit data within network108. Network 108 may further include any number of hardwired and/orwireless connections. For example, building 102 may communicatewirelessly (e.g., via WiFi, ZigBee, cellular, radio, etc.) with atransceiver that is hardwired (e.g., via a fiber optic cable, a CAT5cable, etc.) to other computing devices in network 108.

Still referring to FIG. 1, building data acquisition system 100 is shownto include a building analysis system 110. Building analysis system 110may include one or more electronic devices connected to network 108. Invarious embodiments, building analysis system 110 may be a computerserver (e.g., an FTP server, file sharing server, web server, etc.) or acombination of servers (e.g., a data center, a cloud computing platform,etc.). Building analysis system 110 may include a processing circuitconfigured to perform the functions and processes described herein.

Building analysis system 110 may be configured to obtain performancedata for buildings 102-106 (e.g., either directly from buildings 102-106or from another computing device connected to network 108). Theperformance data may include a plurality of data points. Each of thedata points may include a value for a weather-related predictor variable(e.g., outside air temperature or enthalpy, cooling degree days, heatingdegree days, cooling energy days, heating energy days, etc.) and anassociated energy consumption value for a building or building site. Theperformance data may be received by building analysis system 110periodically, in response to a request for data from building analysissystem 110, in response to receiving a request from a client device 116(e.g., a user operating client device 116 may request that the buildingdata be sent by the computing device), or at any other time.

In some embodiments, building analysis system 110 is configured to modelthe energy usage of buildings 102-106 using the performance data. Inother embodiments, building analysis system receives an energy use modelfor buildings 102-106 from an external source (e.g., within buildingdata acquisition system 100 or otherwise). The building energy use modelgenerated or received by building analysis system 110 may be aparametric model or a non-parametric model. In some embodiments,building analysis system 110 may perform LEAN energy analysis usingreadily available data (e.g., utility billing data, weather data, etc.)to model the energy usage profiles of buildings 102-106 and/or predictan energy cost for buildings 102-106. Building analysis system 110 maygenerate and provide various reports to client 116, which may be locatedwithin one of buildings 102-106 or at another location.

In some embodiments, building analysis system 110 may be implemented atone or more of buildings 102-106. For example, building analysis system110 may be integrated as part of a building automation system (BAS) forbuildings 102-106 (e.g., as part of a centralized BAS or in adistributed implementation). In a distributed implementation,performance data may be shared among the distributed components ofbuilding analysis system 110 via network 108. For example, computingdevices at buildings 102-106 may be configured to collaboratively shareperformance data regarding their respective building's energyconsumption and demand. The sharing of performance data among thebuildings' respective computing devices may be coordinated by one ormore of the devices, or by a remote coordination service (e.g., asupervisory controller or remote server connected to network 108).Building analysis system 110 is described in greater detail withreference to FIG. 3.

Referring now to FIG. 2, an energy use profile 200 for a building orbuilding site is shown, according to an exemplary embodiment. Ingeneral, a number of different factors may affect the energy use of abuilding. For example, weather-related variables such as the airtemperature outside the building may affect the amount of energyrequired to heat or cool the building to a set point temperature. Insome embodiments, the building's energy use profile when cooling thebuilding may differ from the building's energy use profile when heatingthe building. In some embodiments, the energy use model for the buildingincludes parameters relating to both heating and cooling the building(e.g., for a four-parameter model or a five-parameter model). In otherembodiments, the energy use model for the building includes parametersrelating to either heating or cooling the building, but not both (e.g.,for a two-parameter model or a three parameter model).

Energy use profile 200 is shown as an x-y plot with building energy useE plotted along a first axis 202 and outdoor air temperature T_(OA)plotted along a second axis 204. In various embodiments, the building'senergy use E may be an energy consumption (e.g., measured in kWh) or anenergy cost associated with the building's energy consumption. Energyconsumption and/or energy cost information may be obtained, for example,from billing data provided by utility 114. In some embodiments, theoutdoor air temperature T_(OA) may be measured using sensors located ator near the building over a particular time period. Energy use profile200 is shown to include a base energy load E₀ 206, a heating balancepoint T_(bH) 208, a cooling balance point T_(bC) 210, a heating slopeS_(H) 212, and a cooling slope S_(C) 214.

Base energy load E₀ 206 may be a baseline or fixed energy usage thatdoes not depend on the outdoor air temperature T_(OA). For example, baseenergy load E₀ 206 may be a function of the energy consumption of thebuilding's lighting, computer systems, security systems, and other suchelectronic devices in the building. Since the energy consumption ofthese devices does not change as a function of the outdoor airtemperature T_(OA), base energy load E₀ 206 may be used to represent theportion of the building's energy consumption that is not a function ofthe outdoor air temperature T_(OA).

Heating slope S_(H) 212 may correspond to the change in energyconsumption or energy costs that results when the outdoor airtemperature T_(OA) drops below a heating balance point T_(bH) 208 (e.g.,a breakeven temperature). For example, assume that heating balance pointT_(bH) 208 for a building is 55° F. When the outdoor air temperatureT_(OA) is at or above 55° F., only an energy expenditure equal to baseload E₀ 206 may be needed to maintain the internal temperature of thebuilding. However, additional energy may be needed if the outdoor airtemperature T_(OA) drops below 55° F. (e.g., to provide mechanicalheating to the interior of the building). As the outdoor air temperatureT_(OA) decreases, the amount of energy needed to heat the buildingincreases at a rate corresponding to heating slope S_(H) 212.

Cooling slope S_(C) 214 may correspond to the change in energyconsumption or energy costs that result when the outdoor air temperatureT_(OA) rises above a cooling balance point T_(bC) 210 (e.g., a breakeventemperature). For example, assume that cooling balance point T_(bC) 210for a building is 67° F. When the outdoor air temperature T_(OA) is ator below 67° F., only an energy expenditure equal to base load E₀ 206may be needed to maintain the internal temperature of the building.However, additional energy may be needed if the outdoor air temperatureT_(OA) rises above 67° F. (e.g., to provide mechanical cooling to theinterior of the building). As the outdoor air temperature T_(OA)increases, the amount of energy needed to cool the building increases ata rate corresponding to cooling slope S_(C) 214.

Still referring to FIG. 2, energy use profile 200 may be associated witha building or building site having a five-parameter energy use model,where base energy usage E₀ 206, heating balance point T_(bH) 208,cooling balance point T_(bC) 210, heating slope S_(H) 212, and coolingslope S_(C) 214 correspond to the five parameters of the five-parametermodel.

In some embodiments, not all five parameters may be necessary orappropriate to model a building's energy use. For example, if thebuilding is located in a cold climate such that the outdoor airtemperature T_(OA) is never higher than heating balance point T_(bH)208, a two-parameter heating model may be appropriate. Parameters in thetwo-parameter heating model may include base energy load E₀ 206 andheating slope S_(H) 212. An energy profile associated with atwo-parameter heating model may be the portion of energy use profile 200to the left of two-parameter heating line 216.

If the building is located in a hot climate such that the outdoor airtemperature T_(OA) is never lower than cooling balance point T_(bC) 210,a two-parameter cooling model may be appropriate. Parameters in thetwo-parameter cooling model may include base energy load E₀ 206 andcooling slope S_(C) 214. An energy profile associated with atwo-parameter cooling model may be the portion of energy use profile 200to the right of two-parameter cooling line 220.

If the building is located in a moderately cool climate such that theoutdoor air temperature T_(OA) is sometimes below heating balance pointT_(bH) 208 (e.g., T_(OA)<T_(bH)) and sometimes between heating balancepoint T_(bH) 208 and cooling balance point T_(bC) 210 (e.g.,T_(bH)<T_(OA)<T_(bC)), a three-parameter heating model may beappropriate. Parameters in the three-parameter heating model may includebase energy load E₀ 206, heating balance point T_(bH) 208, and heatingslope S_(H) 212. An energy profile associated with a three-parameterheating model may be the portion of energy use profile 200 to the leftof three-parameter heating line 218.

If the building is located in a moderately warm climate such that theoutdoor air temperature T_(OA) is sometimes above cooling balance pointT_(bC) 210 (e.g., T_(OA)>T_(bC)) and sometimes between heating balancepoint T_(bH) 208 and cooling balance point T_(bC) 210 (e.g.,T_(bH)<T_(OA)<T_(bC)), a three-parameter cooling model may beappropriate. Parameters in the three-parameter cooling model may includebase energy load E₀ 206, cooling balance point T_(bC) 210, and coolingslope S_(C) 214. An energy profile associated with a three-parametercooling model may be the portion of energy use profile 200 to the rightof three-parameter cooling line 222.

If the building transitions between supplying heating and cooling at asingle balance point (e.g., the building's heating balance point T_(bH)and cooling balance point T_(bC) are equal), a four parameter model maybe appropriate. The parameters in the four-parameter model may includebase energy load E₀ 206, heating slope S_(H) 212, cooling slope S_(C)214, and a single balance point which is both heating balance pointT_(bH) 208 and cooling balance point T_(bC) 210.

Referring now to FIG. 3, a block diagram illustrating a buildinganalysis system 110 in greater detail is shown, according to anexemplary embodiment. Building analysis system 110 may be configured toobtain energy-related performance data for a building or building site.Building analysis system 110 may test a fit of the performance data tomultiple energy use models for the building or building site (e.g., atwo-parameter model and a three-parameter model). By comparing the fitof the performance data to multiple energy use models having differentnumbers of parameters, building analysis system 110 may determine anappropriate parameter order for the energy use model.

Building analysis system 110 is shown to include a communicationsinterface 302, a user interface I/O 303, and a processing circuit 304.Communications interface 302 may include wired or wireless interfaces(e.g., jacks, antennas, transmitters, receivers, transceivers, wireterminals, etc.) for conducting electronic data communications with thevarious components of building data acquisition system 100 or otherexternal devices or data sources. Data communications may be conductedvia a direct connection (e.g., a wired connection, an ad-hoc wirelessconnection, etc.) or a network connection (e.g., an Internet connection,a LAN, WAN, or WLAN connection, etc.). For example, communicationsinterface 302 can include an Ethernet card and port for sending andreceiving data via an Ethernet-based communications link or network. Invarious embodiments, communications interface 302 can include a WiFitransceiver, a cellular transceiver, or a mobile phone transceiver forcommunicating via a wireless communications network.

Communications interface 302 may receive energy-related performance datafor a building or building site. Performance data may include, forexample, energy consumption data, energy cost data, energy demand data,outside air temperature data, historical weather or meteorological data,pricing or billing data (e.g., from an energy provider), predictedenergy usage data, or other energy-related data associated with abuilding or building site. In some embodiments, the performance dataincludes a plurality of data points including at least oneweather-related predictor variable (e.g., outside airtemperature/enthalpy, cooling degree days, heating degree days, coolingenergy days, heating energy days, etc.).

In some embodiments, communications interface 302 receives an energy usemodel for the building or building site. In other embodiments, buildinganalysis system 110 constructs the energy use model using theenergy-related performance data. In some embodiments, multiple energyuse models may be received or constructed. The multiple energy usemodels may have various numbers of parameters. By comparing the fit ofthe performance data to the various energy use models, building analysissystem 110 may determine an appropriate model parameter order for thebuilding or building site.

Still referring to FIG. 3, building analysis system 110 is shown toinclude a user interface I/O 303. User interface I/O 303 may include oneor more user interface input and/or output devices for facilitating userinteraction with building analysis system 110. User interface I/O 303may include, for example, a local display (e.g., a LCD panel, anelectronic display screen, one or more indicator lights, etc.), akeyboard, a mouse, a printer, a microphone, a speaker, a touch-sensitivepanel, a camera, a scanner, one or more user-operable buttons, dials,sliders, switches, or any other type of user interface device.

User interface I/O 303 may be used to receive input from a user (e.g.,physical input, verbal input, etc.) and to provide output to a user in auser-comprehensible format (e.g., text, numbers, words, sounds, statusindicators, visual displays, printouts, etc.). For example, a user mayinteract with user interface I/O 303 to submit a request for informationregarding the parameter order of a particular building energy use model.Building analysis system 110 may process the user request and providethe user with an output (e.g., a visual display, a textual/graphicaloutput, etc.) indicating the parameter order of the particular buildingenergy use model. As another example, a user may interact with userinterface I/O to request a performance analysis report for a particularbuilding or building system. Building analysis system 110 may processthe request and provide the user with an output (e.g., a visual display,a textual/graphical report, etc.) analyzing the performance of theparticular building or building system.

In various embodiments, user input may be received locally (e.g., viauser interface I/O 303) or remotely (e.g., via a LAN connection, a WANconnection, a network connection, an Internet connection, etc.) from aremote user interface client (e.g., a remote computer, a remote userdevice, etc.). User output may also be provided locally to a userinteracting with building analysis system 110 via user interface I/O 303or remotely to a user interacting with building analysis system 110 viaa remote user interface client (e.g., a remote computer, over a network,etc.). In some embodiments, user input and user output may be sent andreceived via communications interface 302, user interface I/O 303,and/or a combination of both communications interface 302 and userinterface I/O 303.

Still referring to FIG. 3, building analysis system 110 is shown toinclude a processing circuit 304. In some embodiments, processingcircuit 304 is a component of building analysis system 110. In otherembodiments, processing circuit 304 is a component of any othercomputing device or system configured to analyze energy-relatedcharacteristics and/or statistics of a building. In some embodiments,the various components of processing circuit 304 may be distributedacross multiple computing devices or systems.

Processing circuit 304 is shown to include a processor 306 and memory308. Processor 306 can be implemented as one or more microprocessors(e.g., CPUs, GPUs, etc.), an application specific integrated circuit(ASIC), one or more field programmable gate arrays (FPGAs), a circuitcontaining one or more processing components, a group of distributedprocessing components (e.g., processing components in communication viaa data network or bus), circuitry for supporting a microprocessor, orother hardware configured for processing data. Processor 306 may beconfigured to execute computer code stored in memory 308 to complete andfacilitate the activities described herein.

Memory 308 may include one or more devices (e.g., RAM, ROM, solid statememory, hard disk storage, etc.) for storing data and/or computer codefor completing or facilitating the various processes, layers, andmodules of the present disclosure. Memory 308 may include volatilememory or non-volatile memory. Memory 308 may include databasecomponents, object code components, script components, or any other typeof information structure for supporting the various activities andinformation structures of the present disclosure. According to anexemplary embodiment, memory 308 is communicably connected to processor306 via processing circuit 304 and includes computer code for executing(e.g., by processing circuit 304 and/or processor 306) one or moreprocesses described herein. In brief overview, memory 308 is shown toinclude a building data module 310, a weather data module 312, an energyuse model module 314, a hypothesis testing module 316, a regressionstatistic module 318, a test statistic module 320, a parameter orderdetermination module 322, and performance analysis module 324, an outputand client request module 326, and a building control services module328.

Still referring to FIG. 3, memory 308 is shown to include a buildingdata module 310. Building data module 310 may obtain and/or storebuilding data related to buildings 102-106. In some embodiments,building data includes data relating to the physical characteristics ofa building. For example, building data may include data regarding abuilding's geographic location (e.g., street address, city, coordinates,etc.), dimensions (e.g., floor space, stories, etc.), classification(e.g., office space, hospital, school, etc.), building materials, or anyother physical characteristic which may be used to describe a building.

In some embodiments, building data includes energy-related performancedata for buildings 102-106. Energy-related performance data may include,for example energy consumption data (e.g., current energy usage,historical energy usage, predicted energy usage, etc.), measuredtemperatures or other sensory data obtained by one or more sensorydevices of buildings 102-106, and/or control parameters (e.g., setpoints, tuning parameters, threshold values, etc.) used to regulate thetemperature or other variables within buildings 102-106. In someembodiments, building data includes baseline energy consumption data(e.g., a base load E₀), balance point data (e.g., a heating balancepoint T_(bH), a cooling balance point T_(bC), a single balance pointwhich is both the heating balance point T_(bH) and the cooling balancepoint T_(bC), etc.), heating or cooling slope data (e.g., a heatingslope S_(H), a cooling slope S_(C), etc.), or other data describing theparameters used in an energy use model for a particular building orbuilding site.

In some embodiments, building data may include billing data from one ormore utilities (e.g., utility 114) that supply buildings 102-106 with aconsumable resource. For example, building data may include billing datafrom a utility that provides the building with electrical power. Inanother example, building data may include billing data from a utilitythat supplies water to the building.

In some embodiments, building data module 310 uses the building data tocalculate one or more normalized metrics. For example, building datamodule 310 may normalize the building's energy consumption using thebuilding's internal volume or area. The normalized energy consumptionmay be expressed as an energy consumption per unit area

$\left( {{e.g.},\frac{kWh}{{ft}^{2}}} \right)$and/or an energy consumption per unit volume

$\left( {{e.g.},\frac{kWh}{{ft}^{3}}} \right).$The normalized metrics may be used by building analysis system 110 tocompare the energy consumption of buildings having different sizes,areas, and/or volumes.

Still referring to FIG. 3, memory 308 is shown to include a weather datamodule 312. Weather data module 312 may obtain and store weather datafor one or more geographic locations. For example, weather data mayinclude historical, current, or predicted data regarding a location'stemperature (e.g., outside air temperature), humidity, atmosphericpressure, wind speed, precipitable water, or other weather-related data.In some embodiments, weather data may be gathered via sensors located ator near buildings 102-106. In some embodiments, weather data includesTMY data (e.g., TMY2, data, TMY3 data, etc.). Weather data may includeweather data from any number of different time periods having any degreeof granularity. For example, weather data may identify weatherconditions on a monthly, weekly, daily, or hourly level.

In some embodiments, weather data includes a plurality of data pointsincluding a value for at least one weather-related predictor variable.The weather-related predictor variable may be any variable that dependson a weather-related value (e.g., outside air temperature T_(OA),enthalpy, humidity, pressure, wind speed, precipitation level, etc.). Insome embodiments, the weather-related predictor variable may becalculated based on one or more weather-related values. For example, theweather-related predictor variable may be a cooling degree day (CDD)value, a heating degree day (HDD) value, a cooling energy day (CED)value, or a heating energy day (HED) value.

A CDD or HDD value may represent the amount of heating or cooling neededby the building over a period of time. In some embodiments, the CDD andHDD values for a building may be calculated by integrating thedifference between the outside air temperature T_(OA) of the buildingand a given temperature over a period of time. The given temperature maybe a cooling balance point for the building (e.g., cooling balance pointT_(bC) 210) to determine a CDD value, or heating balance point for thebuilding (e.g., heating balance point T_(bH) 208) to determine a HDDvalue. For example, CDD and HDD values for the building over the courseof a month may be calculated as follows:CDD=∫^(month)Max{0,(T _(OA) −T _(bC))}dtHDD=∫^(month)Max{0,(T _(bH) −T _(OA))}dt

In other embodiments, a set reference temperature may be used tocalculate a building's CDD or HDD value instead of the building's actualbalance point. For example, a reference temperature of 65° F. may beused as a fixed value to compare with the building's outdoor airtemperature. CED and HED values may be calculated in a similar mannerusing outside air enthalpy rather than outside air temperature T_(OA).Weather data module 312 may calculate values for one or moreweather-related predictor variables (e.g., CDD, HDD, CED, HED, etc.)using observed weather data values (e.g., outside air temperatureT_(OA), outside air enthalpy, etc.).

Still referring to FIG. 3, memory 308 is shown to include an energy usemodel module 314. Energy use model module 314 may store one or moreenergy use models for a building or building site. The one or moreenergy use models may be of any form. For example, energy use modelmodule 314 may store parametric models (e.g., linear regression models,non-linear regression models, etc.), non-parametric models (neuralnetworks, kernel estimation, hierarchical Bayesian, etc.), or somethingin between (e.g., Gaussian process models). In some embodiments, energyuse model module 314 receives one or more energy use models viacommunications interface 302. In other embodiments, energy use modelmodule 314 generates one or more energy use models using the buildingdata stored in building data module 310 and/or the weather data storedin weather data module 312.

In various embodiments, energy use model module 314 generates atwo-parameter energy use model, a three parameter energy use model, orboth a two-parameter and a three-parameter energy use model. Forbuildings or building sites that have either a heating profile or acooling profile (but not both), hypothesis testing the two-parametermodel and/or the three parameter model may be sufficient to determine anappropriate parameter order (e.g., two or three) for the building'senergy use model. In other embodiments, energy use model module 314generates one or more energy use models having a higher or lowerparameter order (e.g., a single parameter model, a four-parameter model,a five-parameter model, etc.). For buildings or building sites havingboth a heating profile and a cooling profile, the higher order modelsmay be useful in determining an appropriate parameter order.

In some embodiments, energy use model module 314 models the energy useof a building using linear regression. A linear regression model for abuilding may be represented by the following equation:Y=Xβ+e,where Yε

^(n×1) is the building's energy consumption, Xε

^(n×p) is a predictor variable matrix, βε

^(p×1) is a vector of unknown regression coefficients, and e is themodel error such that e˜N(0,t_(i)σ²). The predictor variable matrix Xmay have a size of n×p where p is the total number of predictorvariables (e.g., including the number of days per period t=[t₁ . . .t_(n)]^(T)) and n is the total number of observations.

The predictor variable matrix X may include a weather-related predictorvariable (e.g., outside air temperature T_(OA), enthalpy, cooling degreedays, heating degree days, heating energy days, cooling energy days,etc.). The weather-related predictor variable may be a function of abalance point parameter (e.g., T_(bH), T_(bC), etc.) used to calculateheating degree days or cooling degree days. The balance point parametermay indirectly affect the energy consumption predicted by the energy usemodel by affecting the value of the weather-related predictor variable.In some embodiments, energy use model module 314 uses only oneweather-related predictor variable. Non-weather-related predictorvariables may include, for example, water consumption, buildingoccupancy, days off, the number of days per period t, and/or any othervariable which may affect the building's energy consumption.

Vector β may include one or more regression coefficients (e.g., β₀, β₁,. . . β_(p)) of the energy use model. In some embodiments, eachregression coefficient corresponds to a parameter of the energy usemodel. For example, a one-parameter model may have a single regressioncoefficient β₀ corresponding to a base energy load E₀ model parameter. Atwo-parameter model may have two regression coefficients β₀ and β₁corresponding to a base energy load E₀ model parameter and either aheating slope S_(H) model parameter (e.g., for a two-parameter heatingmodel) or cooling slope S_(C) model parameter (e.g., for a two-parametercooling model). A three-parameter model may have two regressioncoefficients (e.g., β₀ and β₁) as well as a balance point parametercorresponding to either heating a balance point T_(bH) (e.g., for athree-parameter heating model) or cooling balance point T_(bC) (e.g.,for a three-parameter cooling model).

The order of the energy use model may be defined by the number ofparameters θ in the energy use model. Model parameters θ may includeboth explicit model parameters (e.g., regression coefficients β₀, β₁, .. . β_(p)) and non-explicit model parameters (e.g., balance pointparameters T_(bH) and T_(bC)). Non-explicit model parameters may includebalance point parameters and other parameters (i.e., other thanregression coefficients of the energy use model) which contribute to theenergy use predicted by the energy use model by affecting the value ofone or more of the predictor variables in predictor variable matrix X.For example, the value of a balance point parameter (e.g., T_(bH) orT_(bC)) may affect the value of a weather-related predictor variable(e.g., CDD, HDD, etc.) in predictor variable matrix X.

In some embodiments, modeling the energy use E of a building usinglinear regression includes estimating the values of the regression modelcoefficients in vector β. Energy use model module 314 may use any of avariety of different estimation techniques to estimate the values of theregression model coefficients in vector β. In some embodiments, energyuse model module 314 uses a partial least squares regression (PLSR)method. In other embodiments, energy use model module 314 may use othermethods, such as ridge regression (RR), principal component regression(PCR), weighted least squares regression (WLSR), or ordinary leastsquares regression (OLSR).

Generally, a least squares estimation problem can be stated as follows:given a linear modelY=Xβ+e,e˜N(0,t _(i)σ²),find the vector {circumflex over (β)} that minimizes the sum of squarederror RSS, where

${RSS} = {{\sum\limits_{i = 1}^{n}\;{\frac{{\hat{e}}_{i}^{2}}{t_{i}}\mspace{14mu}{and}\mspace{14mu}\hat{e}}} = {{{{Y - {X\;\hat{\beta}}}}}.}}$In the above equations, Y is a vector of size n×1 that contains theindividual n observations of the dependent variable (e.g., energy useE), X is a matrix of size n×p where p is the total number of predictorvariables (e.g., including the number of days per period t=[t₁ . . .t_(n)]^(T)), and e is a normally distributed random vector with zeromean and uncorrelated elements. The optimal value of {circumflex over(β)} based on a least squares estimation has the solution{circumflex over (β)}=(X ^(T) X)⁻¹ X ^(T) Y.Energy use model module 314 may solve the least squares estimationproblem to estimate values for the regression model coefficients invector β.

In some embodiments, energy use model module 314 estimates the modelparameters θ for a two-parameter energy use model and/or athree-parameter energy use model. In a three-parameter energy use model,the model parameters θ may include one more unknown parameter (e.g., aheating balance point T_(bH) or a cooling balance point T_(bC)) than ina two-parameter model. For example, in a two-parameter model, the modelparameters θ may include only the regression model coefficients β (e.g.,θ=β). In a three-parameter model, the model parameters θ may includeboth the regression model coefficients β and either a heating balancepoint T_(bH) or a cooling balance point T_(bC) (e.g., θ=[β T_(b)]^(T)where T_(b) is either T_(bH) or T_(bC). When estimating the modelparameters θ, for the two-parameter model, energy use model module 314may set the model parameter corresponding to the heating balance pointT_(bH) or the cooling balance point T_(bC) to a fixed value. The fixedvalue may be a minimum of the outside air temperature or the outside airenthalpy (e.g., for the cooling balance point T_(bC)) or a maximum ofthe outside air temperature or the outside air enthalpy (e.g., for theheating balance point T_(bH)).

In some embodiments, energy use model module 314 uses outside airtemperature and energy consumption data to estimate the balance points(e.g., {circumflex over (T)}_(bC) and/or {circumflex over (T)}_(bH)).For example, energy use model module 314 may analyze the energyconsumption and outside air temperature data to identify a maximumoutside air temperature (i.e., for heating balance point {circumflexover (T)}_(bH)) or a minimum outside air temperature (i.e., for coolingbalance point {circumflex over (T)}_(bC)) below or above which buildingenergy consumption is a function of the outside air temperature.

According to another embodiment, energy use model module 314 uses anoptimization scheme to determine the balance point or points. Theoptimization scheme may include an exhaustive search of the balancepoints, a gradient descent algorithm, and/or a generalized reducedgradient (GRG) method to estimate balance points {circumflex over(T)}_(bC) and/or {circumflex over (T)}_(bH). In some embodiments, energyuse model module 314 identifies the balance points using an iterativelyreweighted least squares regression method. For example, energy usemodel module 314 may search for balance points that minimize the sum ofsquared error RSS of the building energy use model, where

${RSS} = {{\sum\limits_{i = 1}^{n}\;{\frac{{\hat{e}}_{i}^{2}}{t_{i}}\mspace{14mu}{and}\mspace{14mu}\hat{e}}} = {{{{Y - {X\;\hat{\beta}}}}}.}}$

The model parameters θ may be expressed as a vector of estimates whichincludes the estimated regression coefficients and, in thethree-parameter model, an estimated balance point. In a two-parametermodel, the vector of estimates {circumflex over (θ)} may include onlythe estimated regression model coefficients {circumflex over (β)} (e.g.,{circumflex over (θ)}={circumflex over (β)}). In a three-parametermodel, the vector of estimates {circumflex over (θ)} may include boththe estimated regression model coefficients {circumflex over (β)} andeither a heating balance point estimate {circumflex over (T)}_(bH) or acooling balance point estimate {circumflex over (T)}_(bC) (e.g.,{circumflex over (θ)}=[{circumflex over (β)} {circumflex over(T)}_(b)]^(T), where {circumflex over (T)}_(b) is either {circumflexover (T)}_(bH) or {circumflex over (T)}_(bC)). Once the model parametersθ are estimated, energy use model module 314 may store the energy usemodel or models for use by other components of building analysis system110.

Still referring to FIG. 3, memory 308 is shown to include a hypothesistesting module 316. Hypothesis testing module 316 may receive an energyuse model for a building or building site. In some embodiments, theenergy use model is generated by energy use model module 314, aspreviously described. In other embodiments, the energy use model may bereceived from another memory module, system, process, or otherwiseobtained from any other data source.

In some embodiments, the energy use model is a linear regression modelof the form Y=Xβ+e, where Y is a vector including n observations ofbuilding energy use E, X is a n×p matrix including p predictorvariables, and β is a vector of unknown model parameters. The predictorvariables may include a weather-related predictor variable (e.g.,outside air temperature T_(OA), enthalpy, cooling degree days, heatingdegree days, heating energy days, cooling energy days, etc.). The valuesof the data in vector Y and matrix X (e.g., the building energy use Eand the weather-related predictor variable) may be obtained from thebuilding data stored in building data module 310 and/or theweather-related data stored in weather data module 312.

Hypothesis testing module 316 may be configured to evaluate the buildingenergy use model (e.g., using hypothesis testing) to determine anappropriate parameter order for the building energy use model.Generally, a hypothesis test evaluates the validity of a hypothesis withrespect to a set of data. For example, hypothesis testing module 316 maytest a null hypothesis H₀ against an alternative hypothesis H_(a) withrespect to a set of building performance data (e.g., energy consumptiondata, weather-related data, etc.). Hypothesis testing generally resultsin one of two outcomes: rejection of the null hypothesis or failure toreject the null hypothesis. Failure to reject the null hypothesis doesnot necessarily mean that the null hypothesis is true. The nullhypothesis H₀ should be selected such that rejection of the nullhypothesis is meaningful.

Hypothesis testing module 316 may be configured to formulate a nullhypothesis H₀ and an alternative hypothesis H_(a). In some embodiments,hypothesis testing module 316 formulates a null hypothesis H₀postulating that a two-parameter energy use model is appropriate for aparticular building or building site. Under the null hypothesis H₀, thebuilding energy use model may not have a variable parameter in the setof model parameters θ corresponding to a cooling balance point T_(bC)(e.g., for a two-parameter cooling model) or a heating balance pointT_(bH) (e.g., for a two-parameter heating model). Under the nullhypothesis H₀, either the cooling balance point T_(bC) or the heatingbalance point T_(bH) may be set to a fixed value. The fixed value may bea minimum of the outside air temperature or outside air enthalpy (e.g.,for the cooling balance point T_(bC)) or a maximum of the outside airtemperature or outside air enthalpy (e.g., for the heating balance pointT_(bH)).

The fixed value of the balance point may be used as a substitute for theactual balance point when the actual balance point is unknown and themeasured temperature and/or enthalpy data does not allow the balancepoint to be accurately determined. For example, the fixed value of thecooling balance point T_(bC) may be used to indicate that the actualcooling balance point is less than or equal to the minimum measuredoutside air temperature/enthalpy. The fixed value of the heating balancepoint T_(bH) may be used to indicate that the actual heating balancepoint is greater than or equal to the maximum measured outside airtemperature/enthalpy.

In some embodiments, hypothesis testing module 316 formulates analternative hypothesis H_(a) postulating that a three-parameter energyuse model is appropriate for the particular building or building site.Under the alternative hypothesis H_(a), the building energy use modelmay include a variable parameter (e.g., in the set of model parametersθ) corresponding to a cooling balance point T_(bC) (e.g., for athree-parameter cooling model) or a heating balance point T_(bH) (e.g.,for a three-parameter heating model). Under the alternative hypothesis,the cooling balance point T_(bC) or the heating balance point T_(bH) maybe treated as an unknown parameter.

Still referring to FIG. 3, hypothesis testing module 316 is shown toinclude a regression statistic module 318 and a test statistic module320. Hypothesis testing module 316 may use regression statistic module318 and test statistic module 320 to test the null hypothesis H₀ againstthe alternative hypothesis H_(a) in determining whether to reject thenull hypothesis H₀.

Regression statistic module 318 may be configured to calculate a firstregression statistic for the building energy use model under the nullhypothesis H₀ and a second regression statistic for the building energyuse model under the alternative hypothesis H_(a). The regressionstatistics may indicate a fit of the energy use model to a plurality ofdata points under the null hypothesis H₀ and the alternative hypothesisH_(a). The plurality of data points may include a plurality ofobservations of building energy use and a weather-related predictorvariable. In some embodiments, regression statistic module 318 mayobtain the plurality of data points from the building data stored inbuilding data module 310 and/or the weather-related data stored inweather data module 312.

In some embodiments, the first regression statistic RSS₁ is a residualsum of squares under the null hypothesis H₀ and the second regressionstatistic RSS₂ is a residual sum of squares under the alternativehypothesis H_(a). For example, regression statistic module 318 maycalculate the first and second regression statistics according to thefollowing equations:

${{RSS}_{1} = {{\sum\limits_{i = 1}^{n}\;{\frac{{\hat{e}}_{1,i}^{2}}{t_{i}}\mspace{14mu}{and}\mspace{14mu}{RSS}_{2}}} = {\sum\limits_{i = 1}^{n}\frac{{\hat{e}}_{2,i}^{2}}{t_{i}}}}},$where ê₁ and ê₂ are the residuals resulting from regression under thenull hypothesis H₀ and the alternative hypothesis H_(a), respectively(e.g., ê=∥Y−X{circumflex over (β)}∥), t is the number of days perperiod, and n is the total number of observations.

In some embodiments, the first regression statistic RSS₁ and the secondregression statistic RSS₂ follow a Chi-squared distribution. Asdescribed above, under the null hypothesis H₀, either the coolingbalance point T_(bC) or the heating balance point T_(bH) may be set to afixed value. However, under the alternative hypothesis H_(a), thecooling balance point T_(bC) or the heating balance point T_(bH) may betreated as an unknown parameter. Thus, the degrees of freedom of RSS₁may be equal to df₁=n−p whereas the degrees of freedom of RSS₂ may beequal to df₂=n−p−1, where df₁>df₂. The first regression statistic RSS₁and the second regression statistic RSS₂ may follow a Chi-squareddistribution such that RSS₁˜χ² (n−p) and RSS₂˜χ²(n−p−1).

Still referring to FIG. 3, test statistic module 320 may be configuredto calculate a test statistic based on the first regression statisticRSS₁ and the second regression statistic RSS₂. In some embodiments, thetest statistic is a ratio of (a) an improvement between the firstregression statistic and the second regression statistic to (b) thesecond regression statistic divided by a number of degrees of freedom ofthe second regression statistic. For example, test statistic module 320may calculate the test statistic F_(test) using the following equation:

$F_{test} = {\frac{\frac{{RSS}_{1} - {RSS}_{2}}{{df}_{1} - {df}_{2}}}{\frac{{RSS}_{2}}{{df}_{2}}} \sim {F\left( {{{df}_{1} - {df}_{2}},{df}_{2}} \right)}}$In some embodiments, the test statistic F_(test) has an F-distributionwith degrees of freedom df₁−df₂ and df₂.

Test statistic module 320 may be configured to compare the teststatistic F_(test) with a threshold value. In some embodiments, thethreshold value is retrieved from memory, specified by a user, orotherwise received from a separate system or process. In otherembodiments, test statistic module 320 may calculate the thresholdvalue. For example, test statistic module 320 may calculate thethreshold value F_(critical) using the following equation:F _(critical) =F ⁻¹(1−α,df ₁ −df ₂ ,df ₂)where α is a significance level and F⁻¹ is the inverse of theF-distribution.

Significance level α is the probability of incorrectly rejecting thenull hypothesis H₀ (i.e., incorrect rejection of a true nullhypothesis). Significance level α may be modulated (e.g., between α=0and α=1) to increase or decrease F_(critical) and to adjust the level ofimprovement in F_(test) that warrants rejecting the null hypothesis H₀.In various embodiments, significance level α may be 0.05, 0.10, or anyother value for indicating various levels of improvement which may beconsidered significant. Significance level α may be retrieved frommemory, specified by a user, or received from any other data source.

Still referring to FIG. 3, hypothesis testing module 316 may performhypothesis testing using the test statistic F_(test) and the thresholdvalue F_(critical). In some embodiments, hypothesis testing module 316may compare the test statistic F_(test) with the threshold valueF_(critical). If the test statistic is less than the threshold value(e.g., F_(test)<F_(critical)), hypothesis testing module 316 maydetermine that the hypothesis testing has failed to reject the nullhypothesis H₀. Conversely, if the test statistic is not less than thethreshold value (e.g., F_(test)≧F_(critical)), hypothesis testing module316 may determine that the hypothesis testing has rejected the nullhypothesis H₀. Hypothesis testing module 316 may output or store aresult of the hypothesis testing for use by parameter orderdetermination module 322.

Still referring to FIG. 3, memory 308 is shown to include a parameterorder determination module 322. Parameter order determination module 322may be configured to determine an appropriate parameter order for thebuilding energy use model based on a result of the hypothesis testingperformed by hypothesis testing module 316. In some embodiments, failingto reject the null hypothesis H₀ may indicate that the parameter ordercorresponding to the alternative hypothesis H_(a) is not significantlybetter for modeling the energy usage of the building or building sitethan the parameter order corresponding to the null hypothesis H₀ (e.g.,the improvement between the first regression statistic RSS₁ and thesecond regression statistic RSS₂ is not significant). Conversely,rejecting the null hypothesis H₀ may indicate that the parameter ordercorresponding to the alternative hypothesis H_(a) is significantlybetter for modeling the energy usage of the building or building sitethan the parameter order corresponding to the null hypothesis H₀ (e.g.,the improvement between the first regression statistic RSS₁ and thesecond regression statistic RSS₂ is significant).

In some embodiments, parameter order determination module 322 maydetermine an appropriate parameter order based on the model parameterorders corresponding to the null hypothesis H₀ and/or the alternativehypothesis H_(a). For example, if the null hypothesis H₀ corresponds toa two-parameter energy use model and the alternative hypothesis H_(a)corresponds to a three-parameter energy use model, rejecting the nullhypothesis H₀ may indicate that the three-parameter model issignificantly better in describing the energy use of the building orbuilding site than the two-parameter model.

In some embodiments, parameter order determination module 322 maydetermine that a two-parameter energy use model is appropriate inresponse to failing to reject the null hypothesis H₀. In someembodiments, parameter order determination module 322 may determine thata three-parameter energy use model is appropriate in response torejecting the null hypothesis H₀. In other embodiments, parameter orderdetermination module 322 may determine that any other parameter order isappropriate based on the parameter orders corresponding to the nullhypothesis H₀ and/or the alternative hypothesis H_(a).

In some embodiments, parameter order determination module 322 isconfigured to identify a current parameter order of the energy usemodel. Parameter order determination module 322 may compare the currentparameter order with the appropriate parameter order to determinewhether the current order matches the appropriate parameter order.Parameter order determination module 322 may be configured to update theenergy use model with an energy use model having the appropriateparameter order in response to the current parameter order not matchingthe appropriate parameter order. For example, if the current energy usemodel for a building site is a three-parameter model and parameter orderdetermination module 322 determines that a two-parameter model isappropriate, parameter order determination module 322 may update thecurrent energy use model with a two-parameter energy use model.Parameter order determination module 322 may store and/or output anenergy use model having the appropriate parameter order.

Still referring to FIG. 3, memory 308 is shown to include a performanceanalysis module 324. Performance analysis module 324 may be configuredto analyze a building's energy performance using a building energy usemodel (e.g., the energy use model stored by parameter orderdetermination module 322). Performance analysis module 324 may beconfigured to perform a variety of energy analysis functions including,for example, generating energy savings estimates, detecting outlierbuilding sites with poor energy performance (e.g., by comparing similarbuilding sites), and determining the effects of a fault on a building'senergy consumption.

In some embodiments, performance analysis module 324 may perform energyanalysis using a minimal amount of building performance data (e.g., aLEAN energy analysis). Performance analysis module 324 may rely on thenumber and value of parameters θ in the building energy use model toarrive at conclusions regarding a building's energy performance. Byensuring that the energy use model for a building has an appropriatenumber of parameters θ, the accuracy of the conclusions reached byperformance analysis module 324 may be improved.

In some embodiments, performance analysis module 324 is configured toperform outlier detection. Performance analysis module 324 may beconfigured to compare one or more statistics of a test building to theprobability distribution of those statistics for the other buildings inthe same class (e.g., buildings having similar usage characteristics,buildings located in similar geographic regions, buildings modeled byenergy use models having the same number of parameters, etc.). Forexample, performance analysis module 324 may determine that a building'sstatistic is an outlier for the class based on a number of standarddeviations that the statistic is above or below the mean for the classdistribution. In various embodiments, performance analysis module 324may use any number of outlier detection techniques to identify anoutlier value. For example, performance analysis module 324 may use ageneralized extreme studentized deviate test (GESD), Grubb's test, orany other form of univariate outlier detection technique. In someembodiments, performance analysis module 324 may identify a building asan outlier if the statistic for the building is within a fixedpercentage of the minimum or maximum for the class distribution (e.g.,top 5%, bottom 5%, top 10%, etc.).

In some embodiments performance analysis module 324 may use a distancevalue between statistics to detect an outlier. For example, performanceanalysis module 324 may determine a Gaussian or Mahalanobis distance tocompare statistics. Such a distance may represent a statistical distanceaway from the typical building in the class. If the Mahalanobis distancefor a test building is above a critical value, performance analysismodule 324 may generate an indication that the building's one or morestatistics are outliers in relation to the other buildings in the class.In some embodiments, performance analysis module 324 may project thedistance onto the vector directions defining changes in a building'sparameters to determine the root cause. Other outlier detectiontechniques that may be used by performance analysis module 324 include,but are not limited to, Wilkes' method (e.g., if multivariate analysisis used) and various cluster analysis techniques.

Performance analysis module 324 may be configured to detect excessiveenergy consumption by a building. In some embodiments, performanceanalysis module 324 may perform one or more hypothesis tests using thebuilding data stored in building data module 310 and the energy usemodel stored by parameter order determination module 322 and/or energyuse model module 314 to detect excessive energy consumption. Exemplaryhypothesis tests include F-tests and Chi-squared tests. In someembodiments, hypothesis testing may be used to test one or more valuesagainst a baseline, as described in U.S. patent application Ser. No.13/252,092 entitled “Systems and Methods for Detecting Changes in EnergyUsage In a Building” and filed on Oct. 3, 2011, the entirety of which isincorporated by reference herein.

In some embodiments, performance analysis module 324 may be configuredto determine the effects of a fault on a building's energy consumption.In various embodiments, performance analysis module 324 may determineone or more changes to the model parameters of the energy use model(e.g., changes to the parameters in parameter vector β) that result whena particular fault is present. For example, performance analysis module324 may determine changes to the vector of model parameters β thatresult from a damper being stuck in the open position. In oneembodiment, performance analysis module 324 uses a simulation model todetermine the changes to the energy use model parameters. In anotherembodiment, performance analysis module 324 determines a mapping betweenchanges to a building's energy use model parameters and its physicalparameters (e.g., the building's cooling slope S_(C), heating slopeS_(H), cooling balance point T_(bC), etc).

Performance analysis module 324 may provide the changes to the energyuse model parameters to energy use model module 314. Energy use modelmodule 314 may then determine a corresponding change to the building'senergy consumption. For example, a stuck damper of an AHU may cause abuilding's normalized annual energy consumption to increase by 25,000kWh/year. Performance analysis module 324 may use this change in energyconsumption to calculate a corresponding financial cost associated withthe fault condition. For example, performance analysis module 324 maymultiply the determined change in energy consumption by a price per unitenergy (e.g., received from utility 114) to calculate a financial costassociated with the fault.

In some embodiments, performance analysis module 324 may be configuredto perform fault detection and analysis of the building under studyusing the energy use model generated by energy use model module 314and/or the updated energy model stored by parameter order determinationmodule 322. In one embodiment, performance analysis module 324 maymonitor changes to the building's energy use model's parameters overtime to detect potential faults. In another embodiment, performanceanalysis module 324 may perform fault detection using peer analysis withother buildings in its class to detect potential faults. For example,buildings having outlier model parameter changes may be identified ashaving potential faults. If a potential fault is detected, performanceanalysis module 324 may use a mapping between energy use modelparameters and the building's physical parameters to determine the causeof the fault. Advantageously, determining an appropriate order for thebuilding energy use model (e.g., by parameter order determination module322) may facilitate the various energy analysis functions performed byperformance analysis module 324.

Still referring to FIG. 3, memory 308 is shown to include an output andclient request module 326. Output and client request module 326 may beconfigured to process user input received via communications interface302 and/or user interface I/O 303. For example, output and clientrequest module 326 may process a user request for information regardingthe parameter order or appropriate parameter order for a specificbuilding energy use model. As another example, output and client requestmodule 326 may process a user request to run a performance analysisand/or generate an analytical performance analysis report for aparticular building or building system. Output and client request module326 may be configured to run or query parameter order determinationmodule 322, energy use model module 314, performance analysis module324, or any other component of building analysis system 110 to determinea response to the user request.

Output and client request module 326 may be configured to generate anoutput for presentation to a user. Output and client request module 326may generate a graphical display, a visual display, a textual display,or any other type of user-comprehensible output. Output and clientrequest module 326 may communicate a result of a user query/request(e.g., an appropriate parameter order of a particular building energyuse model, an analytical report, etc.), a result of an intermediateprocessing step (e.g., a test statistic or regression statistic value,etc.), a result of a performance analysis, a result of a fault detectionanalysis, or any other data stored or used by building analysis system110. In various embodiments, output and client request module 326 maygenerate display data for presentation via a local display (e.g., to alocal user interacting with building analysis system 110 via userinterface I/O 303), or may communicate output data to a remote user viacommunications interface 302 (e.g., a user interacting with buildinganalysis system 110 via a network connection and/or a remote client).

Still referring to FIG. 3, memory 308 is shown to include a buildingcontrol services module 328. Building control services module 328 may beconfigured to control one or more buildings, building systems, orbuilding subsystems using a building energy use model. For example,building control services module 328 may utilize closed loop control,feedback control, PI control, model predictive control, or any othertype of automated building control methodology that relies on a model totranslate an input into an output. In some embodiments, building controlservices module 328 uses the building energy use model updated byparameter order determination module 322 to have the appropriate modelparameter order to translate an input received from a building systeminto an output or control signal for the building system.

Building control services module 328 may receive inputs from sensorydevices (e.g., temperature sensors, pressure sensors, flow rate sensors,humidity sensors, electric current sensors, cameras, radio frequencysensors, microphones, etc.), user input devices (e.g., computerterminals, client devices, user devices, etc.) or other data inputdevices via communications interface 302 and/or user interface I/O 303.Building control services module 328 may apply the various inputs to abuilding energy use model to determine an output for one or morebuilding control devices (e.g., dampers, air handling units, chillers,boilers, fans, pumps, etc.) in order to affect a variable state orcondition within a building or building system associated with thebuilding energy use model (e.g., zone temperature, humidity, air flowrate, etc.). Building control services module 328 may operate thebuilding or building system to maintain building conditions (e.g.,temperature, humidity, air quality, etc.) within a setpoint range, tooptimize energy performance (e.g., to minimize energy consumption, tominimize energy cost, etc.), and/or to satisfy any constraint orcombination of constraints as may be desirable for variousimplementations.

Referring now to FIG. 4, a flowchart of a process 400 for determining anappropriate parameter order for a building energy use model is shown,according to an exemplary embodiment. In some embodiments, process 400is performed by building analysis system 110 using one or more of memorymodules 310-324, as described with reference to FIG. 3. In someembodiments, process 400 may be used to determine whether atwo-parameter energy use model or a three-parameter energy use model isappropriate for a particular building or building site.

Process 400 is shown to include receiving an energy use model for abuilding site (step 402). The energy use model may be of any formincluding parametric models (e.g., linear regression models, non-linearregression models, etc.), non-parametric models (neural networks, kernelestimation, hierarchical Bayesian, etc.), or something in between (e.g.,Gaussian process models). In some embodiments, step 402 includesreceiving an energy use model from an external source (e.g., viacommunications interface 302). In other embodiments, step 402 includesgenerating the energy use model (e.g., using the building data stored inbuilding data module 310 and/or the weather data stored in weather datamodule 312).

In some embodiments, linear regression is used in step 402 to generatethe energy use model. A linear regression model for a building site maybe represented by the following equation:Y=Xβ+e,where Yε

^(n×1) is the site's energy consumption, Xε

^(n×p) is a predictor variable matrix, βε

^(p×1) is a vector of unknown regression coefficients, and e is themodel error such that e˜N(0,t_(i)σ²). The predictor variable matrix Xmay have a size of n×p where p is the total number of predictorvariables (e.g., including the number of days per period t=[t₁ . . .t_(n)]^(T)) and n is the total number of observations.

In some embodiments, the energy use model includes a weather-relatedpredictor variable (e.g., outside air temperature T_(OA), enthalpy,cooling degree days, heating degree days, heating energy days, coolingenergy days, etc.). In some embodiments, the energy use model includesonly one weather-related predictor variable. In some embodiments, theenergy use model includes one or more non-weather-related predictorvariables. Non-weather-related predictor variables may include, forexample, water consumption, building occupancy, days off, the number ofdays per period t, and/or any other variable which may affect the site'senergy consumption. The weather-related predictor variable and/or otherpredictor variables may be included in predictor variable matrix X.

In some embodiments, generating a linear regression energy use modelincludes estimating the values of the regression coefficients in vectorβ. Any of a variety of different estimation techniques may be used toestimate the values of the regression coefficients in vector β. In someembodiments, step 402 includes using a partial least squares regression(PLSR) method. In other embodiments, other methods (e.g., ridgeregression (RR), principal component regression (PCR), weighted leastsquares regression (WLSR), ordinary least squares regression (OLSR),etc.) may be used to estimate the values of the regression coefficientsin vector β.

Still referring to FIG. 4, process 400 is shown to include obtaining aplurality of data points (step 404). Each of the data points may includea value of the weather-related predictor variable and an associatedenergy consumption value for the building site. In some embodiments, theplurality of data points are received prior to generating the energy usemodel and may be used to perform the linear regression described withreference to step 402.

The weather-related predictor variable may be any variable that has aweather-related value (e.g., outside air temperature T_(OA), enthalpy,humidity, pressure, wind speed, precipitation level, etc.) or anyvariable that depends on a weather-related value. In some embodiments,the weather-related predictor variable may be calculated based on one ormore weather-related values. In some embodiments, step 404 includesreceiving at least one of an observed temperature value and an observedenthalpy value and calculating the value of the weather-relatedpredictor variable using the observed temperature value or the observedenthalpy value.

For example, the weather-related predictor variable may be a coolingdegree day (CDD) value, a heating degree day (HDD) value, a coolingenergy day (CED) value, or a heating energy day (HED) value. A CDD orHDD value may generally represent the amount of heating or coolingneeded by the building over a period of time. In some embodiments, theCDD and HDD values for a building may be calculated by integrating thedifference between the outside air temperature T_(OA) of the buildingand a given temperature over a period of time. The given temperature maybe a cooling balance point for the building (e.g., cooling balance pointT_(bC)) to determine a CDD value, or heating balance point for thebuilding (e.g., heating balance point T_(bH)) to determine a HDD value.For example, CDD and HDD values for the building over the course of amonth may be calculated as follows:CDD=∫^(month)Max{0,(T _(OA) −T _(bC))}dtHDD=∫^(month)Max{0,(T _(bH) −T _(OA))}dt

In other embodiments, a set reference temperature may be used tocalculate a building's CDD or HDD value instead of the building's actualbalance point. For example, a reference temperature of 65° F. may beused as a fixed value to compare with the building's outdoor airtemperature. CED and HED values may be calculated in a similar mannerusing outside air enthalpy rather than outside air temperature T_(OA).

Still referring to FIG. 4, process 400 is shown to include calculating afirst regression statistic indicating a fit of the energy use model tothe plurality of data points under a null hypothesis H₀ and a secondregression statistic indicating a fit of the energy use model to theplurality of data points under an alternative hypothesis H_(a) (step406).

The null hypothesis H₀ may postulate that a two-parameter energy usemodel is appropriate for a particular building or building site. In someembodiments, under the null hypothesis H₀, the building energy use modelmay not have a variable parameter in θ corresponding to a coolingbalance point T_(bC) (e.g., for a two-parameter cooling model) or aheating balance point T_(bH) (e.g., for a two-parameter heating model).In other embodiments, under the null hypothesis H₀, either the coolingbalance point T_(bC) or the heating balance point T_(bH) may be set to afixed value. The fixed value may be a minimum of the measured values foroutdoor air temperature or enthalpy (e.g., for the cooling balance pointT_(bC)) or a maximum of the measured values for outdoor air temperatureor enthalpy (e.g., for the heating balance point T_(bH)).

The alternative hypothesis H_(a) may postulate that a three-parameterenergy use model is appropriate for the particular building or buildingsite. Under the alternative hypothesis H_(a), the building energy usemodel may include a variable parameter in θ corresponding to a coolingbalance point T_(bC) (e.g., for a three-parameter cooling model) or aheating balance point T_(bH) (e.g., for a three-parameter heatingmodel). Under the alternative hypothesis, the cooling balance pointT_(bC) or the heating balance point T_(bH) may be treated as an unknownparameter.

The first regression statistic and the second regression statistic maybe represented by RSS₁ and RSS₂, respectively. In some embodiments, RSS₁and RSS₂ are calculated by regression statistic module 318, aspreviously described with reference to FIG. 3. In some embodiments, thefirst regression statistic RSS₁ is a residual sum of squares under thenull hypothesis H₀ and the second regression statistic RSS₂ is aresidual sum of squares under the alternative hypothesis H_(a). Forexample, RSS₁ and RSS₂ may be calculated using the following equations:

${{RSS}_{1} = {{\sum\limits_{i = 1}^{n}\;{\frac{{\hat{e}}_{1,i}^{2}}{t_{i}}\mspace{14mu}{and}\mspace{14mu}{RSS}_{2}}} = {\sum\limits_{i = 1}^{n}\frac{{\hat{e}}_{2,i}^{2}}{t_{i}}}}},$where ê₁ and ê₂ are the residuals resulting from regression under thenull hypothesis H₀ and the alternative hypothesis H_(a), respectively(e.g., ê=∥Y−X{circumflex over (β)}∥), t is the number of days perperiod, and n is the total number of observations.

The degrees of freedom of RSS₁ may be equal to df₁=n−p and the degreesof freedom of RSS₂ may be equal to df₂=n−p−1, where df₁>df₂. The firstregression statistic RSS₁ and the second regression statistic RSS₂ mayfollow a Chi-squared distribution such that RSS₁˜χ² (n−p) and RSS₂˜χ²(n−p−1).

Still referring to FIG. 4, process 400 is shown to include comparing atest statistic to a threshold value (step 408). Step 408 may beperformed by test statistic module 320, as previously described withreference to FIG. 3. The test statistic may be a function of the firstregression statistic RSS₁ and the second regression statistic RSS₂. Insome embodiments, the test statistic is a ratio of (a) an improvementbetween the first regression statistic RSS₁ and the second regressionstatistic RSS₂ to (b) the second regression statistic RSS₂ divided by anumber of degrees of freedom of the second regression statistic df₂.

In some embodiments, the test statistic is specified by a user orreceived as an input to process 400. In other embodiments, step 408includes calculating the test statistic. For example, the test statisticF_(test) may be calculated using the following equation:

$F_{test} = {\frac{\frac{{RSS}_{1} - {RSS}_{2}}{{df}_{1} - {df}_{2}}}{\frac{{RSS}_{2}}{{df}_{2}}} \sim {F\left( {{{df}_{1} - {df}_{2}},{df}_{2}} \right)}}$In some embodiments, the test statistic F_(test) has an F-distributionwith degrees of freedom df₁−df₂ and df₂.

Step 408 may include receiving a threshold value. In some embodiments,the threshold value is retrieved from memory, specified by a user, orotherwise received from a separate system or process. In otherembodiments, step 408 includes calculating the threshold value. Forexample, the threshold value F_(critical) may be calculated using thefollowing equation:F _(critical) =F ⁻¹(1−α,df ₁ −df ₂ ,df ₂)where α is a significance level and F⁻¹ is the inverse of theF-distribution.

Significance level α is the probability of incorrectly rejecting thenull hypothesis H₀ (i.e., incorrect rejection of a true nullhypothesis). Significance level α may be modulated (e.g., between α=0and α=1) to increase or decrease F_(critical) and to adjust the level ofimprovement in F_(test) that is warrants rejecting the null hypothesisH₀. In various embodiments, significance level α may be 0.05, 0.10, orany other value for indicating various levels of improvement which maybe considered significant. Significance level α may be retrieved frommemory, specified by a user, or received from any other data source.

Still referring to FIG. 4, process 400 is shown to include determiningan appropriate parameter order for the energy use model based on aresult of the comparison (step 410). In some embodiments, step 410includes rejecting the null hypothesis H₀ if the result of thecomparison reveals that test statistic is not less than the thresholdvalue (e.g., F_(test)≧F_(critical)). In some embodiments, step 410includes failing to reject the null hypothesis H₀ if the result of thecomparison reveals that the test statistic is less than the thresholdvalue (e.g., F_(test)<F_(critical)).

In some embodiments, failing to reject the null hypothesis H₀ mayindicate that the parameter order corresponding to the alternativehypothesis H_(a) is not significantly better for modeling the energyusage of the building or building site than the parameter ordercorresponding to the null hypothesis H₀ (e.g., the improvement betweenthe first regression statistic RSS₁ and the second regression statisticRSS₂ is not significant). Conversely, rejecting the null hypothesis H₀may indicate that the parameter order corresponding to the alternativehypothesis H_(a) is significantly better for modeling the energy usageof the building or building site than the parameter order correspondingto the null hypothesis H₀ (e.g., the improvement between the firstregression statistic RSS₁ and the second regression statistic RSS₂ issignificant).

In some embodiments, step 410 includes determining that a two-parameterenergy use model is appropriate in response to failing to reject thenull hypothesis H₀. In some embodiments, step 410 includes determiningthat a three-parameter energy use model is appropriate in response torejecting the null hypothesis H₀. In some embodiments, step 410 includesidentifying the building site as at least one of: a building site forwhich heating is not required and a building site for which cooling isnot required if the null hypothesis H₀ is rejected.

The identification of the building site as a site for which heating orcooling is not required may be specific to the range of outside airtemperatures and/or enthalpies represented in the weather data andspecific to the sources of energy consumption modeled in the buildingenergy use model. For example, identifying a building site as a site forwhich heating or cooling is not required may indicate that there is norange of temperatures in the measured weather data for which the energyconsumption represented in the energy use model is not a function ofoutside air temperature (e.g., no flat region in the graph shown in FIG.2). Thus, an identification of a building site as a site for whichheating or cooling is not required may indicate only that the sources ofenergy consumption modeled in the building energy use model are notneeded to heat or cool the building for the range of temperatures and/orenthalpies represented in the measured weather data upon which theenergy consumption model is based. Other sources of heating or coolingnot captured in the energy use model may be used to provide heating orcooling for the building site.

Still referring to FIG. 4, process 400 is shown to include flagging theenergy use model if the current parameter order of the energy use modeldoes not match the appropriate parameter order (step 412). Step 412 mayinclude identifying a current parameter order of the energy use modeland comparing the current parameter order with the appropriate parameterorder. For example, if the current energy use model for a building siteis a three-parameter model and it is determined in step 410 that atwo-parameter model is appropriate, step 412 may include flagging,marking, tagging, or otherwise indicating that the current energy usemodel has an inappropriate parameter order. In some embodiments, step412 may be performed when the null hypothesis H₀ is rejected. Step 412may include outputting and/or storing an energy use model having theappropriate parameter order.

Still referring to FIG. 4, process 400 is shown to include updating theenergy use model in response to a determination that the energy usemodel has an inappropriate parameter order (step 414). In variousembodiments, step 414 may include determining whether the energy usemodel was flagged as having an inappropriate parameter order in step412, determining whether the current parameter order of the energy usemodel matches the appropriate parameter order for the energy use model,determining whether the null hypothesis H₀ is rejected, or any otherdetermination that would indicate that the current model parameter orderis inappropriate.

Step 414 may include updating the current energy use model with anenergy use model that has the appropriate parameter order. For example,if the current energy use model for a building site is a three-parametermodel and it is determined in step 410 that a two-parameter model isappropriate, step 414 may include updating the energy use model to be atwo-parameter model. Step 414 may include adding one or more parametersto the energy use model, subtracting/removing one or more parametersfrom the energy use model, and/or updating the value of one or moreexisting parameters in the building energy use model.

Still referring to FIG. 4, process 400 is shown to include applyinginputs to the updated energy use model (step 416). Inputs may include,for example, inputs from sensory devices (e.g., temperature sensors,pressure sensors, flow rate sensors, humidity sensors, electric currentsensors, cameras, radio frequency sensors, microphones, etc.), userinput devices (e.g., computer terminals, client devices, user devices,etc.) or other data input devices via communications interface 302and/or user interface I/O 303. Inputs may include measured variablesindicating a current state or condition within a building or buildingsystem, setpoints, constraint conditions, control parameters, operatingschedules, or other measured, calculated, or user-defined inputs.

Step 416 may include using the updated energy use model to translate theinputs into an output or control signal for the building system. Forexample, step 416 may include using closed loop control, feedbackcontrol, PI control, model predictive control, or any other type ofautomated building control methodology that relies on a model totranslate an input into an output or control signal. In someembodiments, step 416 includes using a building energy use model thathas been updated to have the appropriate model parameter order totranslate an input received from a building system into an output orcontrol signal for the building system.

Step 416 may include applying the various inputs to a building energyuse model to determine an output for one or more building controldevices (e.g., dampers, air handling units, chillers, boilers, fans,pumps, etc.) in order to affect a variable state or condition within abuilding or building system associated with the building energy usemodel (e.g., zone temperature, humidity, air flow rate, etc.). Step 416may include operating the building or building system to maintainbuilding conditions (e.g., temperature, humidity, air quality, etc.)within a setpoint range, to optimize energy performance (e.g., tominimize energy consumption, to minimize energy cost, etc.), and/or tosatisfy any constraint or combination of constraints as may be desirablefor various implementations.

Still referring to FIG. 4, process 400 is shown to include conducting aperformance analysis using the updated energy use model (step 418). Insome embodiments, step 418 is performed by performance analysis module324 as previously described with reference to FIG. 3. Step 418 mayinclude analyzing a building's energy performance using the updatedbuilding energy use model to generate energy savings estimates, detectoutlier building sites with poor energy performance (e.g., by comparingsimilar building sites), determine the effects of a fault on abuilding's energy consumption, or perform other energy analysis tasks

In some embodiments, step 418 includes performing an energy analysisusing a minimal amount of building performance data (e.g., a LEAN energyanalysis). Step 418 may include using the number and value of parametersθ in the building energy use model to arrive at conclusions regarding abuilding's energy performance. By ensuring that the energy use model fora building has an appropriate number of parameters, the accuracy of theconclusions reached in step 418 may be improved.

In some embodiments, step 418 includes performing outlier detection. Forexample, step 418 may include comparing one or more statistics of a testbuilding to the probability distribution of those statistics for theother buildings in the same class (e.g., buildings having similar usagecharacteristics, buildings located in similar geographic regions,buildings modeled by energy use models having the same number ofparameters, etc.). Step 418 may include determining that a building'sstatistic is an outlier for the class based on a number of standarddeviations that the statistic is above or below the mean for the classdistribution. In various embodiments, step 418 includes using any numberof outlier detection techniques to identify an outlier value. Forexample, step 418 may include using a generalized extreme studentizeddeviate test (GESD), Grubb's test, or any other form of univariateoutlier detection technique. In some embodiments, step 418 includesidentifying a building as an outlier if the statistic for the buildingis within a fixed percentage of the minimum or maximum for the classdistribution (e.g., top 5%, bottom 5%, top 10%, etc.).

In some embodiments step 418 includes using a distance value betweenstatistics to detect an outlier. For example, step 418 may includedetermining a Mahalanobis distance to compare statistics. Such adistance may represent a statistical distance away from the typicalbuilding in the class. If the Mahalanobis distance for a test buildingis above a critical value, step 418 may include generating an indicationthat the building's one or more statistics are outliers in relation tothe other buildings in the class. In some embodiments, step 418 includesprojecting the distance onto the vector directions defining changes in abuilding's parameters to determine the root cause. Other outlierdetection techniques that may be used in step 418 include, but are notlimited to, Wilkes' method (e.g., if multivariate analysis is used) andvarious cluster analysis techniques.

Step 418 may include detecting excessive energy consumption by abuilding. In some embodiments, step 418 includes performing one or morehypothesis tests using the building data stored in building data module310 and the energy use model stored by parameter order determinationmodule 322 and/or energy use model module 314 to detect excessive energyconsumption. Exemplary hypothesis tests include F-tests and Chi-squaredtests. In some embodiments, hypothesis testing may be used to test oneor more values against a baseline.

In some embodiments, step 418 includes determining the effects of afault on a building's energy consumption. In various embodiments, step418 includes determining one or more changes to the model parameters θof the energy use model that result when a particular fault is present.For example, step 418 may include determining changes to the modelparameters θ that result from a damper being stuck in the open position.In one embodiment, step 418 includes using a simulation model todetermine the changes to the energy use model parameters θ. In anotherembodiment, step 418 includes determining a mapping between changes to abuilding's energy use model parameters and its physical parameters(e.g., the building's cooling slope S_(C), heating slope S_(H), coolingbalance point T_(bC), etc.). In some embodiments, only the regressioncoefficients in vectorβ β are used in fault detection and peer analysisregardless of whether the energy use model is a two-parameter model or athree-parameter model. However, knowing whether the data correspond to atwo-parameter model or a three-parameter model may yield more reliablevalues for the regression model coefficients β, thereby providing a morereliable fault detection or peer analysis.

Step 418 may include providing the changes to the energy use modelparameters to energy use model module 314. Energy use model module 314may then determine a corresponding change to the building's energyconsumption. For example, a stuck damper of an AHU may cause abuilding's normalized annual energy consumption to increase by 25,000kWh/year. Performance analysis module 324 may use this change in energyconsumption to calculate a corresponding financial cost associated withthe fault condition. For example, performance analysis module 324 maymultiply the determined change in energy consumption by a price per unitenergy (e.g., received from utility 114) to calculate a financial costassociated with the fault.

In some embodiments, step 418 includes performing fault detection andanalysis of the building under study using the updated building energyuse model. In one embodiment, step 418 includes monitoring changes tothe building's energy use model's parameters over time to detectpotential faults. In another embodiment, step 418 includes performingfault detection using peer analysis with other buildings in its class todetect potential faults. For example, buildings having outlier modelparameter changes may be identified as having potential faults. If apotential fault is detected, step 418 may include using a mappingbetween energy use model parameters and the building's physicalparameters to determine the cause of the fault. Advantageously,determining an appropriate order for the building energy use model(e.g., by parameter order determination module 322) may facilitate thevarious energy analysis functions performed in step 418.

Still referring to FIG. 4, process 400 is shown to include providing anoutput using a result of the performance analysis (step 420). In someembodiments, step 420 includes generating display data for presentationto a user via a local display (e.g., to a local user interacting withbuilding analysis system 110 via user interface I/O 303). In someembodiments, step 420 includes communicating a result of the performanceanalysis to a remote user, system, or device via communicationsinterface 302 (e.g., a user interacting with building analysis system110 via a network connection and/or a remote client). Step 420 mayinclude generating an output for presentation to a user in auser-comprehensible format (e.g., visual display, graphical display,textual display, etc.) and/or storing a result of the performanceanalysis in a data storage device.

In some embodiments, step 420 includes using a result of the performanceanalysis to determine or change an output or control signal provided toa building system device. Step 420 may include providing the output forone or more building control devices (e.g., dampers, air handling units,chillers, boilers, fans, pumps, etc.) in order to affect a variablestate or condition within a building or building system associated withthe building energy use model (e.g., zone temperature, humidity, airflow rate, etc.). Step 420 may include operating the building orbuilding system to maintain building conditions (e.g., temperature,humidity, air quality, etc.) within a setpoint range, to optimize energyperformance (e.g., to minimize energy consumption, to minimize energycost, etc.), and/or to satisfy any constraint or combination ofconstraints as may be desirable for various implementations.

Embodiments of the subject matter and the operations described in thisspecification can be implemented in digital electronic circuitry, or incomputer software embodied on a tangible medium, firmware, or hardware,including the structures disclosed in this specification and theirstructural equivalents, or in combinations of one or more of them.Embodiments of the subject matter described in this specification can beimplemented as one or more computer programs, i.e., one or more modulesof computer program instructions, encoded on one or more computerstorage medium for execution by, or to control the operation of, dataprocessing apparatus. Alternatively or in addition, the programinstructions can be encoded on an artificially-generated propagatedsignal, e.g., a machine-generated electrical, optical, orelectromagnetic signal, that is generated to encode information fortransmission to suitable receiver apparatus for execution by a dataprocessing apparatus. A computer storage medium can be, or be includedin, a computer-readable storage device, a computer-readable storagesubstrate, a random or serial access memory array or device, or acombination of one or more of them. Moreover, while a computer storagemedium is not a propagated signal, a computer storage medium can be asource or destination of computer program instructions encoded in anartificially-generated propagated signal. The computer storage mediumcan also be, or be included in, one or more separate components or media(e.g., multiple CDs, disks, or other storage devices). Accordingly, thecomputer storage medium may be tangible and non-transitory.

The operations described in this specification can be implemented asoperations performed by a data processing apparatus on data stored onone or more computer-readable storage devices or received from othersources.

The term “client or “server” include all kinds of apparatus, devices,and machines for processing data, including by way of example aprogrammable processor, a computer, a system on a chip, or multipleones, or combinations, of the foregoing. The apparatus can includespecial purpose logic circuitry, e.g., an FPGA (field programmable gatearray) or an ASIC (application-specific integrated circuit). Theapparatus can also include, in addition to hardware, code that createsan execution environment for the computer program in question, e.g.,code that constitutes processor firmware, a protocol stack, a databasemanagement system, an operating system, a cross-platform runtimeenvironment, a virtual machine, or a combination of one or more of them.The apparatus and execution environment can realize various differentcomputing model infrastructures, such as web services, distributedcomputing and grid computing infrastructures.

A computer program (also known as a program, software, softwareapplication, script, or code) can be written in any form of programminglanguage, including compiled or interpreted languages, declarative orprocedural languages, and it can be deployed in any form, including as astand-alone program or as a module, component, subroutine, object, orother unit suitable for use in a computing environment. A computerprogram may, but need not, correspond to a file in a file system. Aprogram can be stored in a portion of a file that holds other programsor data (e.g., one or more scripts stored in a markup languagedocument), in a single file dedicated to the program in question, or inmultiple coordinated files (e.g., files that store one or more modules,sub-programs, or portions of code). A computer program can be deployedto be executed on one computer or on multiple computers that are locatedat one site or distributed across multiple sites and interconnected by acommunication network.

The processes and logic flows described in this specification can beperformed by one or more programmable processors executing one or morecomputer programs to perform actions by operating on input data andgenerating output. The processes and logic flows can also be performedby, and apparatus can also be implemented as, special purpose logiccircuitry, e.g., an FPGA (field programmable gate array) or an ASIC(application specific integrated circuit).

Processors suitable for the execution of a computer program include, byway of example, both general and special purpose microprocessors, andany one or more processors of any kind of digital computer. Generally, aprocessor will receive instructions and data from a read-only memory ora random access memory or both. The essential elements of a computer area processor for performing actions in accordance with instructions andone or more memory devices for storing instructions and data. Generally,a computer will also include, or be operatively coupled to receive datafrom or transfer data to, or both, one or more mass storage devices forstoring data, e.g., magnetic, magneto-optical disks, or optical disks.However, a computer need not have such devices. Moreover, a computer canbe embedded in another device, e.g., a mobile telephone, a personaldigital assistant (PDA), a mobile audio or video player, a game console,a Global Positioning System (GPS) receiver, or a portable storage device(e.g., a universal serial bus (USB) flash drive), to name just a few.Devices suitable for storing computer program instructions and datainclude all forms of non-volatile memory, media and memory devices,including by way of example semiconductor memory devices, e.g., EPROM,EEPROM, and flash memory devices; magnetic disks, e.g., internal harddisks or removable disks; magneto-optical disks; and CD-ROM and DVD-ROMdisks. The processor and the memory can be supplemented by, orincorporated in, special purpose logic circuitry.

To provide for interaction with a user, embodiments of the subjectmatter described in this specification can be implemented on a computerhaving a display device, e.g., a CRT (cathode ray tube), LCD (liquidcrystal display), OLED (organic light emitting diode), TFT (thin-filmtransistor), plasma, other flexible configuration, or any other monitorfor displaying information to the user and a keyboard, a pointingdevice, e.g., a mouse, trackball, etc., or a touch screen, touch pad,etc., by which the user can provide input to the computer. Other kindsof devices can be used to provide for interaction with a user as well;for example, feedback provided to the user can be any form of sensoryfeedback, e.g., visual feedback, auditory feedback, or tactile feedback;and input from the user can be received in any form, including acoustic,speech, or tactile input. In addition, a computer can interact with auser by sending documents to and receiving documents from a device thatis used by the user; for example, by sending web pages to a web browseron a user's client device in response to requests received from the webbrowser.

Embodiments of the subject matter described in this specification can beimplemented in a computing system that includes a back-end component,e.g., as a data server, or that includes a middleware component, e.g.,an application server, or that includes a front-end component, e.g., aclient computer having a graphical user interface or a Web browserthrough which a user can interact with an embodiment of the subjectmatter described in this specification, or any combination of one ormore such back-end, middleware, or front-end components. The componentsof the system can be interconnected by any form or medium of digitaldata communication, e.g., a communication network. Examples ofcommunication networks include a local area network (“LAN”) and a widearea network (“WAN”), an inter-network (e.g., the Internet), andpeer-to-peer networks (e.g., ad hoc peer-to-peer networks).

While this specification contains many specific embodiment details,these should not be construed as limitations on the scope of anyinventions or of what may be claimed, but rather as descriptions offeatures specific to particular embodiments of particular inventions.Certain features that are described in this specification in the contextof separate embodiments can also be implemented in combination in asingle embodiment. Conversely, various features that are described inthe context of a single embodiment can also be implemented in multipleembodiments separately or in any suitable subcombination. Moreover,although features may be described above as acting in certaincombinations and even initially claimed as such, one or more featuresfrom a claimed combination can in some cases be excised from thecombination, and the claimed combination may be directed to asubcombination or variation of a subcombination.

Similarly, while operations are depicted in the drawings in a particularorder, this should not be understood as requiring that such operationsbe performed in the particular order shown or in sequential order, orthat all illustrated operations be performed, to achieve desirableresults. In certain circumstances, multitasking and parallel processingmay be advantageous. Moreover, the separation of various systemcomponents in the embodiments described above should not be understoodas requiring such separation in all embodiments, and it should beunderstood that the described program components and systems cangenerally be integrated together in a single software product embodiedon a tangible medium or packaged into multiple such software products.

Thus, particular embodiments of the subject matter have been described.Other embodiments are within the scope of the following claims. In somecases, the actions recited in the claims can be performed in a differentorder and still achieve desirable results. In addition, the processesdepicted in the accompanying figures do not necessarily require theparticular order shown, or sequential order, to achieve desirableresults. In certain embodiments, multitasking and parallel processingmay be advantageous.

What is claimed is:
 1. A method for determining an appropriate parameterorder for an energy use model for a building site, the methodcomprising: receiving an energy use model for the building site at acommunications interface of a building analysis system, the energy usemodel comprising a weather-related predictor variable; obtaining, by aprocessing circuit of the building analysis system, a plurality of datapoints, each of the data points comprising a value of theweather-related predictor variable and an associated energy consumptionvalue for the building site; calculating, by the processing circuit, afirst regression statistic indicating a fit of the energy use model tothe plurality of data points under a null hypothesis that the energy usemodel has a first parameter order and a second regression statisticindicating a fit of the energy use model to the plurality of data pointsunder an alternative hypothesis that the energy use model has a secondparameter order different from the first parameter order; generating, bythe processing circuit, a test statistic that is a ratio comprising animprovement between the first regression statistic and the secondregression statistic; comparing, by the processing circuit, the teststatistic to a threshold value to determine whether the improvementwarrants rejecting the null hypothesis; determining, by the processingcircuit, an appropriate parameter order for the energy use model basedon a result of the comparison; receiving, at the processing circuit,inputs from one or more sensors that measure a variable state orcondition of the building site; using the energy use model with theappropriate parameter order to generate, by the processing circuit,control signals for one or more building control devices as a functionof the inputs from the sensors; and operating the building controldevices according to the control signals, wherein operating the buildingcontrol devices affects the variable state or condition of the buildingsite.
 2. The method of claim 1, wherein obtaining the plurality of datapoints comprises, for each of the data points: receiving at least oneof: an observed temperature value and an observed enthalpy value; andcalculating the value of the weather-related predictor variable usingthe observed temperature value or the observed enthalpy value.
 3. Themethod of claim 1, wherein the energy use model includes a balance pointparameter under the alternative hypothesis and does not include abalance point parameter under the null hypothesis.
 4. The method ofclaim 3, wherein the balance point parameter is at least one of: atemperature parameter having a temperature value between a minimum and amaximum of a plurality of observed temperature values, and an enthalpyparameter having an enthalpy value between a minimum and a maximum of aplurality of observed enthalpy values.
 5. The method of claim 1, furthercomprising analyzing energy consumption data and weather data toidentify a balance point parameter for use in the energy use model,wherein: under the null hypothesis, the balance point parameter isidentified by using an extremum of the weather data as the balance pointparameter; and under the alternative hypothesis, the balance pointparameter is identified by determining a range of the weather datawithin which the energy consumption data is a function of the weatherdata and using an extremum of the determined range as the balance pointparameter.
 6. The method of claim 3, wherein the value of theweather-related predictor variable is a function of the balance pointparameter.
 7. The method of claim 1, wherein the weather-relatedpredictor variable is at least one of: cooling degree days, heatingdegree days, cooling energy days, heating energy days, temperature, andenthalpy.
 8. The method of claim 1, wherein the energy use model underthe null hypothesis is nested within the energy use model under thealternative hypothesis.
 9. The method of claim 1, wherein the firstregression statistic is a sum of squared error under the null hypothesisand the second regression statistic is a sum of squared error under thealternative hypothesis, wherein the sum of squared error is a functionof a difference between an energy consumption of the building sitepredicted by the energy use model and an actual energy consumption ofthe building site.
 10. The method of claim 1, wherein the test statisticis a ratio of (a) an improvement between the first regression statisticand the second regression statistic to (b) the second regressionstatistic divided by a number of degrees of freedom of the secondregression statistic.
 11. The method of claim 1, further comprising:identifying a significance level; and calculating the threshold value,wherein the threshold value is a function of the identified significancelevel.
 12. The method of claim 11, wherein the function of theidentified significance level is an inverse F-distribution functionbased on: the identified significance level; a difference between anumber of degrees of freedom of the first regression statistic and anumber of degrees of freedom of the second regression statistic; andnumber of degrees of freedom of the second regression statistic.
 13. Themethod of claim 1, wherein determining the appropriate parameter orderfor the energy use model comprises: rejecting the null hypothesis if theresult of the comparison reveals that test statistic is not less thanthe threshold value; and failing to reject the null hypothesis if theresult of the comparison reveals that the test statistic is less thanthe threshold value.
 14. The method of claim 13, wherein determining theappropriate parameter order for the energy use model further comprises:determining that a three-parameter model is appropriate in response torejecting the null hypothesis; and determining that a two-parametermodel is appropriate in response to failing to reject the nullhypothesis.
 15. The method of claim 13, wherein determining anappropriate parameter order for the energy use model further comprises:identifying a range of weather data values used by the energy use modelto predict energy consumption; and determining that the energyconsumption predicted by the energy use model is a function of theweather data values for weather data values within the identified range.16. The method of claim 13, wherein determining an appropriate parameterorder for the energy use model further comprises: in response to failingto reject the null hypothesis, identifying the building site as at leastone of: a building site for which heating is not required and a buildingsite for which cooling is not required.
 17. The method of claim 1,further comprising: identifying a current parameter order of the energyuse model; comparing the current parameter order with the appropriateparameter order; updating the energy use model with an energy use modelhaving the appropriate parameter order in response to the currentparameter order not matching the appropriate parameter order; andstoring the energy use model for the building site, wherein the storedenergy use model has the appropriate parameter order.
 18. The method ofclaim 17, further comprising: using the stored energy use model toperform a peer analysis of energy use model parameters for a class ofbuildings; calculating a difference between an energy use modelparameter of the stored energy use model and a mean of the energy usemodel parameters for the class of buildings; and detecting an outliermodel parameter based on a result of the calculation.
 19. The method ofclaim 17, further comprising: monitoring changes to one or more energyuse model parameters in the stored energy use model; detecting theexistence of a fault condition using a monitored change to the energyuse model parameters; and determining a change to an energy consumptionthat results from the fault condition based on the change to the energyuse model parameters.
 20. The method of claim 1, further comprising:updating the energy use model with an energy use model that has theappropriate parameter order; applying inputs to the updated energy usemodel; conducting a performance analysis using the updated energy usemodel; and providing an output using a result of the performanceanalysis.
 21. A system for determining an appropriate parameter orderfor an energy use model for a building site, the system comprising: oneor more sensors that measure a variable state or condition of thebuilding site; a communications interface that receives an energy usemodel for the building site, the energy use model comprising aweather-related predictor variable; a processing circuit comprising aprocessor and memory, wherein the processing circuit: obtains aplurality of data points, each of the data points comprising a value ofthe weather-related predictor variable and an associated energyconsumption value for the building site; calculates a first regressionstatistic indicating a fit of the energy use model to the plurality ofdata points under a null hypothesis that that energy use model has afirst parameter order and a second regression statistic indicating a fitof the energy use model to the plurality of data points under analternative hypothesis that the energy use model has a second parameterorder different from the first parameter order; generates a teststatistic that is a ratio comprising an improvement between the firstregression statistic and the second regression statistic; compares atest statistic to a threshold value to determine whether the improvementwarrants rejecting the null hypothesis; determines an appropriateparameter order for the energy use model based on a result of thecomparison; receives inputs from the one or more sensors that measurethe variable state or condition of the building site; and uses theenergy use model with the appropriate parameter order to generatecontrol signals as a function of the inputs from the sensors; andbuilding control devices that operate according to the control signalsand affect the variable state or condition of the building site.
 22. Thesystem of claim 21, wherein obtaining the plurality of data pointscomprises, for each of the data points: receiving at least one of: anobserved temperature value and an observed enthalpy value; andcalculating the value of the weather-related predictor variable usingthe observed temperature value or the observed enthalpy value.
 23. Thesystem of claim 21, wherein the energy use model includes a balancepoint parameter under the alternative hypothesis and does not include abalance point parameter under the null hypothesis.
 24. The system ofclaim 23, wherein the balance point parameter is at least one of: atemperature parameter having a temperature value between a minimum and amaximum of a plurality of observed temperature values, and an enthalpyparameter having an enthalpy value between a minimum and a maximum of aplurality of observed enthalpy values.
 25. The system of claim 23,wherein the value of the weather-related predictor variable is afunction of the balance point parameter.
 26. The system of claim 21,wherein the first regression statistic is a sum of squared error underthe null hypothesis and the second regression statistic is a sum ofsquared error under the alternative hypothesis, wherein the sum ofsquared error is a function of a difference between an energyconsumption of the building site predicted by the energy use model andan actual energy consumption of the building site.
 27. The system ofclaim 21, wherein the processing circuit: identifies a significancelevel; and calculates the threshold value, wherein the threshold valueis a function of the identified significance level.
 28. The system ofclaim 21, wherein determining the appropriate parameter order for theenergy use model comprises: rejecting the null hypothesis if the resultof the comparison reveals that test statistic is not less than thethreshold value; and failing to reject the null hypothesis if the resultof the comparison reveals that the test statistic is less than thethreshold value.
 29. The system of claim 28, wherein determining theappropriate parameter order for the energy use model further comprises:determining that a three-parameter model is appropriate in response torejecting the null hypothesis; and determining that a two-parametermodel is appropriate in response to failing to reject the nullhypothesis.
 30. The system of claim 27, wherein determining anappropriate parameter order for the energy use model further comprises:identifying a range of weather data values used by the energy use modelto predict energy consumption; and determining that the energyconsumption predicted by the energy use model is a function of theweather data values for weather data values within the identified range.31. The system of claim 28, wherein determining an appropriate parameterorder for the energy use model further comprises: in response to failingto reject the null hypothesis, identifying the building site as at leastone of: a building site for which heating is not required and a buildingsite for which cooling is not required.
 32. The system of claim 21,wherein the processing circuit is further: identifies a currentparameter order of the energy use model; compares the current parameterorder with the appropriate parameter order; updates the energy use modelwith an energy use model having the appropriate parameter order inresponse to the current parameter order not matching the appropriateparameter order; and stores the energy use model for the building site,wherein the stored energy use model has the appropriate parameter order.33. The system of claim 21, wherein the processing circuit: updates theenergy use model with an energy use model having the appropriate order;applies inputs to the updated energy use model; conducts a performanceanalysis using the updated energy use model; and provides an outputusing a result of the performance analysis.